Given the line below.
Graph image attached
a. Using variables, write out the formula for the point-slope form of the equation.
b. Determine the slope of the line.
c. Identify the point (-1,-2) as (x1, y1).
d. Write the equation of the line in point-slope form.
Show all work on how you found the slope or determined the slope from the graph. Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
Answers
(a) A point-slope form of the line is y - y₁ = m(x - x₁)
(b) The slope of the line is 2.
(c) The point (x₁, y₁) = (-1, -2).
(d) The equation of a line in point-slope form is y + 2 = 2(x + 1).
What is point-slope form?The formula for a straight line: y - y₁ = m(x - x₁), where m is the slope of the line and (x₁, y₁) is the coordinates of a specific point on the line
(a) Let the two points are (x₁, y₁) and (x₂, y₂)
Then the slope of the lines is given as
m = (y₂ - y₁)/ (x₂ - x₁)
The point-slope form of the line is given as
(y - y₁) = [(y₂ - y₁)/ (x₂ - x₁)] (x-x₁)
y - y₁ = m(x - x₁)
(b) From the graph, (x₁, y₁) = (-1, -2) and (x₂, y₂) = (1, 2)
So, slope = (2 -(-2))/ (1-(-1))
= (2+2)/ (1+1)
= 4/2
= 2
c) (x₁, y₁) = (-1, -2)
d) The equation of a line in point-slope form is given as
y - (-2) = 2(x- (-1))
y + 2 = 2(x + 1)
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Related Questions
What is the GCF of 12, 48, 36, 24, and 60. Will mark BRAINLIEST!!!!!
Answers
Answer: 6
Step-by-step explanation:
Answer: Hi the answer to your question would be
GCF = 12
for the values 12, 24, 36, 48, 60
Here is an explanation!
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Then the greatest common factor is 12.
Hope this helps Ihsan!
Can someone help? :)
Answers
The slope is [tex]\frac{3}{4}[/tex]
What is slope ?
A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not. Any two clearly separated points on a line can be used to calculate the slope of any line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.
here the given two pints are
[tex](x_1,y_1)=(-2,4)\\(x_2,y_2)=(6,10)[/tex]
Now using slope formula,
slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = [tex]\frac{10-4}{6+2}[/tex]
=> slope m = [tex]\frac{6}{8}[/tex]
=> slope m = [tex]\frac{3}{4}[/tex]
Therefore the slope is [tex]\frac{3}{4}[/tex].
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Select all of the scenarios below that correctly identify the independent variable. A. Charlie gets paid by the hour. The number of hours he works is the independent variable. B. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable. C. How much Caleb weighs is relative to the amount he eats. The amount he weighs is the independent variable. D. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.
Answers
Independent varible are variable that dosent depend on any factor that afftect the scenarios.
the scenarios that identify the independent variable.
A. Charlie gets paid by the hour. The number of hours he works is the independent variable.
B. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable.
D. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.
A graden plot 4m by 12m has one side along the fence.The area of the garden is to be doubled by digging a border of uniform width on the other three sides.What should the width of the border be?
Answers
The width of the border is 6 m after digging a border of uniform width on the other three sides.
Step 1:
Original garden plot is 4 m by 12 m. The 12 m side is against the wall.
A border of length D is along three sides of the plot (the 4th side is the wall).
Step 2
area of original garden plot is 12 x 4 = 48 [tex]m^{2}[/tex]
area of new plot = 96 [tex]m^{2}[/tex] (twice the original plot)
96 = (4 + D) (12 + 2D)
Set up equation for the area of the new area of the new plot (double the area of the old garden plot).
Step 3
96 = (4 + D) (12 + 2D)
[tex]96 = 2d^{2}+12d+4(2d+12)[/tex]
[tex]96 = 2d^{2}+12d+8d+48[/tex]
[tex]96 = 2d^{2}+20d+48[/tex]
[tex]96 -2d^2-20d-48 = 0[/tex]
[tex]48-2d^2-20d = 0[/tex]
[tex]-2(d^2+10d-24) = 0[/tex]
d = -12
Now solve for D
Step 4
D = 6 meters
Ignore negative answer because border must be a positive number. So Border is -12 [tex]m^{2}[/tex] (6 m).
Hence the answer is the width of the border is 6 m after digging a border of uniform width on the other three sides.
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Find the radian measure of θ if θ is a central angle in a circle of radius r=14in and θ cuts off an arc length s=7π in
Answers
The formula for determining the length of an arc is experessed as
arc length = θ x r
where
θ is the central angle
r is the radius of the circle
From the information given,
arc length = 7π in
r = 14 in
By substituting these values into the formula,
7π in = θ x 14 in
We would divide both sides of the equation by 14 in. We have
7π in/14 in = θ x 14 in/14 in
θ = π/2
What is the annual percentage yield (APY) for money invested at an annual rate of(A) 4.09% compounded monthly?(B) 4.1% compounded quarterly?
Answers
The annual percentage yield is given by the following formula:
[tex]\text{APY}=(1+\frac{r}{n})^n-1[/tex]Where r is the stated annual interest rate (in decimal form) and n is the number of times compounded.
A) APY for money invested at an annual rate of 4.09% compounded monthly.
Thus, the annual interest rate in decimal form is:
[tex]r=\frac{4.09\%}{100\%}=0.0409[/tex]And as it is compounded monthly then n=12.
Replace these values and solve:
[tex]\begin{gathered} \text{APY}=(1+\frac{0.0409}{12})^{12}-1 \\ \text{APY}=(1+0.0034)^{12}-1 \\ \text{APY}=(1.0034)^{12}-1 \\ \text{APY}=1.0417-1 \\ \text{APY}=0.0417 \end{gathered}[/tex]The APY is 0.0417=4.17%.
B) 4.1% compounded quarterly:
The annual interest rate is:
[tex]r=\frac{4.1\%}{100\%}=0.041[/tex]As it is compounded quarterly then n=4.
Replace and solve:
[tex]\begin{gathered} \text{APY}=(1+\frac{0.041}{4})^4-1 \\ \text{APY}=(1+0.0103)^{12}-1 \\ \text{APY}=(1.0103)^{12}-1 \\ \text{APY}=1.1302-1 \\ \text{APY}=0.1302 \end{gathered}[/tex]The APY is 0.1302=13.02%
Order these numbers from least to greatest. 143 7 7.116, 6.67 20
Answers
We are given the following numbers
[tex]7\frac{1}{9},\: 7.116,\: \frac{143}{20},\: 6.67[/tex]We are asked to arrange these numbers from least to greatest.
As you can see, the numbers are in different forms (decimal, fraction)
So, first we need to convert them into a single form then we can compare them
Let us convert all the numbers into decimals
[tex]\begin{gathered} 7\frac{1}{9}=\frac{7\cdot9+1}{9}=\frac{63+1}{9}=\frac{64}{9}=7.111 \\ \frac{143}{20}=7.15 \end{gathered}[/tex]So the order from least to greatest is
6.67, 7.111, 7.116, 7.15
Now write the numbers in their original form
[tex]undefined[/tex]In the equation (x + 4)^2 = 49, if x equals 3 what is another solution for x?
Please answer quickly.
Answers
if gh=53 and hi=7 then gi=
Answers
In the given line, the length of the line gi is 60 units.
What is a line?A line is an indefinitely long, straight object that is drawn with a minimum width in geometry but is said to have no specific width in mathematics since it lacks depth.An angle is created when two straight lines or rays intersect at a single terminal. The vertex of an angle is the location where the two rays meet.So, the length of gi will be:
We know that,
gh = 53hi = 7Now, we can easily see that the given line is:
gi = gh + higi = 53 + 7gi = 60Therefore, in the given line, the length of the line gi is 60 units.
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Find the measure of the angles between the hands of the clocks at a) 8:54 b) 5:11 and c) 8:03I have the answers, but I need an explanation
Answers
I will explain to you through a drawing on how to identify 3 types of angles :
You will find the angles by placing a protractor aligning the centre with 0:00 marking the hour and the minute will be your angle formed on the watch, you can twist and turn the protractor but it will always form a measured angle .
What is the equation of the line that passes through the point (-3,-6) and has a slope of 1/3
Answers
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
How can I locate a slope?You may determine the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two points. The increase divided by the run is the slope.The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) expressions of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.Formula m = rise / run = y2 - y1 / x2 - x1m = slope
(x1, y1) = coordinates of first point in the line
(x2, y2) = coordinates of second point in the line
Point (-3, 6) (-3, 6) Summary: An equation for the line through the point, which has the undefined slope m specified. x = -3 at the location (-3, 6).To Learn more About line's slope refer to:
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What is the third term of the recursive sequence below
Answers
Given the sequence:
[tex]\begin{gathered} a_1=-6 \\ a_n=\frac{1}{2}a_{n-1}-n \end{gathered}[/tex]Let's find the third term of the sequence.
To find the third term, a3, we have:
First find the second term, a2:
[tex]\begin{gathered} a_2=\frac{1}{2}a_{2-1}-2 \\ \\ a_2=\frac{1}{2}a_1-2 \\ \\ a_2=\frac{1}{2}(-6)-2 \\ \\ a_2=-3-2 \\ \\ a_2=-5 \end{gathered}[/tex]The second term is -5.
To find the third term, we have:
[tex]\begin{gathered} a_3=\frac{1}{2}a_{3-1}-3 \\ \\ a_3=\frac{1}{2}a_2-3 \\ \\ a_3=\frac{1}{2}(-5)-3 \\ \\ a_3=-2.5-3 \\ \\ a_3=-5.5 \end{gathered}[/tex]Therefore, the third term of the
What two numbers add to give 3 and multiply to give -18
Answers
-3 and 6
Explanation:
-3 + 6 = 3
-3 • 6 = -18
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It Carlos sits 3 feet from the fulcrum of a see-saw, how far from the fulcrum must his baby-sister who weighs three-times his weight sit?
A. 1 foot
B. 6 feet
C. 3 feet
D. 9 feet
Answers
Answer: B: 6 feet
Step-by-step explanation: To solve this problem, we need to use the concept of leverage, which is the force applied to an object at a distance from its pivot point. In this case, Carlos is applying a force of 3 feet from the fulcrum, while his baby sister is applying a force 3 times as large, at a distance from the fulcrum.
To find the distance from the fulcrum that the baby sister must sit, we need to balance the forces applied by Carlos and his sister. This means that the product of the force applied by Carlos and the distance from the fulcrum must be equal to the product of the force applied by his sister and the distance from the fulcrum where she must sit.
We can use this information to write the equation: 3 * 3 = 3 * x
Where x is the distance from the fulcrum where the baby sister must sit. We can solve for x by dividing both sides of the equation by 3 to get: x = 6
Therefore, the baby sister must sit 6 feet from the fulcrum in order to balance the forces applied by Carlos and his sister. The correct answer is B. 6 feet.
If Jamal treated his family with a family brunch and the brunch costs $250 and the sales tax was 4%. If Jamal left an 18% tip on the $250. How much did he pay in total?
Answers
The total amount jamal paid is $305.
Given:
Jamal treated his family with a family brunch at the cost of $250.
The sales tax was 4%.
The tip is 18%.
to find the sales tax.
[tex]\begin{gathered} =250\cdot4\text{ \%} \\ =250\cdot\frac{4}{100} \\ =\frac{1000}{100} \\ =10 \end{gathered}[/tex]The amount he paid for sales tax is $ 10.
to find the tip.
[tex]\begin{gathered} =250\cdot18\text{ \%} \\ =250\cdot\frac{18}{100} \\ =\frac{4500}{100} \\ =45 \end{gathered}[/tex]Jamal left a tip of $45.
Thus the total amount paid by Jamal is,
[tex]250+10+45=305[/tex]What's the length of the hypotenuse of a right triangle if the length of one leg is 7 units and the length of the other leg is 14 units?
Answers
ANSWER:
The hypotenuse is
[tex]7\sqrt[]{5}=15.65[/tex]STEP-BY-STEP EXPLANATION:
In this case we can calculate the value of the hypotenuse by means of the Pythagorean theorem.
[tex]\begin{gathered} h^2=a^2+b^2 \\ a=7 \\ b=14 \end{gathered}[/tex]replacing
[tex]\begin{gathered} h^2=7^2+14^2 \\ h^2=49+196 \\ h=\sqrt[]{245} \\ h=7\sqrt[]{5}=15.65 \end{gathered}[/tex]How do I get the answers to thisQuestion 1 - 4
Answers
Answer:
Lines d and e are parallel and lines s and t are also parallel
1. Alternate Exterior Angles Theorem
2. Corresponding Angles Postulate
3. Alternate Angles Postulate
4. Co-interior Angles Theorem
Explanation:
Given the below;
1. Given that;
[tex]\angle1\cong\angle4[/tex]The theorem that justifies the above is the Alternate Exterior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
2. Given that;
[tex]\angle2\cong\angle3[/tex]The theorem that justifies the above is the Corresponding Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the corresponding angles are congruent.
3. Given that;
[tex]\angle6\cong\angle7[/tex]The theorem that justifies the above is the Alternate Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate angles are congruent.
4. Given that;
[tex]m\angle5+m\angle8=180[/tex]The theorem that justifies the above is the Co-interior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, angles that are in the same similar position are supplementary, that is, they add up to 180 degrees.
Sel 9.5.37 Assigned Media Question Help D You, a A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 17 feet more than the length of the shortest side. Find the dimensions if the perimeter is 153 feet. What is the length of the shortest side?
Answers
First we can set the equations we already know
[tex]a\text{ +b +c = 153 ft}[/tex]Where a, b and c are the sides of the triangle. Then, I will assign "a" the shortes side. One side is twice the shortest side so:
[tex]b\text{ = 2a }[/tex]Now, the sentence says, the third side is 17 feet longer that the shortes side "a":
[tex]c\text{ = a + 17}[/tex]Now we have a system of three equations with three unknown variables, so it will be easy to find the value of all the variables. If we put "b" and "c" in the first equation we have:
[tex]a\text{ + (2a) + (a+17) = 153 ft}[/tex][tex]\begin{gathered} 4a\text{ = 153-17} \\ 4a\text{ = }136 \\ a\text{ = 136/4} \\ a=34 \end{gathered}[/tex]Now, since we assigned "a" as the shortest side, we are done.
How many one and one-sixths are in five and five-sixths?
Answers
Using operations of fractions, the answer obtained is
There are 5 [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
What is fraction?
Suppose there is a collection of objects and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator,
Let there are x [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
[tex]1\frac{1}{6} x = 5\frac{5}{6}\\\frac{7}{6}x = \frac{35}{6}\\x = \frac{35}{6} \times \frac{6}{7}\\x = 5[/tex]
There are 5 [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
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The next model of a sports car will cost 6.2% less than the current model. The current model costs $57,000. How much will the price decrease in dollars? What will be the price of the next model
Answers
Answer:
The price will decrease $3534
The price of the next model is $53466
Step-by-step explanation:
57000 divided by 100 and then time 6.2 = $3534
Then subtract 57000 - 3534 = $53466
Answer: 53,466
Step-by-step explanation:
Do 57,000 minus 6.2 or and get 53,466.
Given the end points of A(-8,-2) and B(6,19). The segment AB is divided into the ratio atAR:RB in a 2:5 ratio. Find the coordinates of point R.R=
Answers
The given coordinates in the question are
[tex]\begin{gathered} A=(-8,-2)\text{ = x1=-8, y1=-2} \\ B=(6,19)\text{ = x}2=6,y2=19 \end{gathered}[/tex]Let the coordinate at R be
[tex]R=(x,y)[/tex]The ratio of the line segment given is
[tex]AR\colon RB=2\colon5\text{ (m=2,n=5)}[/tex]The formula to calculate the coordinate of a line segment in a given ratio is given below as
[tex](x,y)=(\frac{mx_2+nx_1}{m+n}),(\frac{my_2+ny_1}{m+n})[/tex][tex]undefined[/tex]–5 = –3(h − 10) + –8
Answers
Answer:
h = 9
Step-by-step explanation:
-5 = -3(h - 10) + (-8)
−5 = −3h + 22
−3h + 22 = −5
−3h = −27
h = 9
--------------
check
-5 = -3(9-10)+(-8)
-5 = -27 + 30 - 8
- 5 = -5
the answer is good
help meeeeeeeeee pleasee
Answers
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
The bull in Ms. Garcia's pasture weighs 0.95 tons. What is the weight of the bull in pounds?
Answers
Answer:
The bull weighs 1,900 pounds.
Step-by-step explanation:
2,000 pounds = 1 ton
0.95 x 2,000 = 1,900 pounds
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Answer: 1,900 pounds
Step-by-step explanation:
There are 2,000 pounds in a ton, so we will multiply 0.95 tons by 2,000 to figure out the weight of the bull in pounds.
0.95 * 2,000 = 1,900 pounds
Yesterday jack drove 38 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unit rate for mile per gallon
Answers
Answer:
the unit rate for miles per gallons is 32.4 miles per gallon
Step-by-step explanation:
From the information we have, Jack drove 401/2 miles and used a total of 1 1/4 gallons of gasoline.
We need to find out how many miles he travelled per each gallon.
40 1/2 miles can be written as 40.5 miles
1 1/4 gallons can be written as 1.25 gallons.
So now we form an equation.
40.5 = 1.25
x = 1
Where x is the number of miles per gallon
We cross multiply the equation
40.5 * 1 = 1.25 * x
40.5 = 1.25x
40.5 / 1.25 = x
32.4 = x
x = 32 .4
Write the standard form of the equation
1) through: (-5, 3) and (2,-2)
Answers
W. Checkpoint: Solve lines 1) Tell whether each equation has exactly one solution, infinitely many solutions, or no solutions no exactly one solution Infinitely many solutions solutions 7(x-2) 9x - 2 9x + 3 = 3(3x + 1) 3x + 2 = 7(x-2)
Answers
7(x-2) = 9x - 2
open the parenthesis
7x - 14 = 9x - 2
collect like term
9x - 7x = -14 + 2
2x = -12
Divide both-side of the equation by 2
x = -6
It has exactly one solution
9x+3 =3(3x+1)
9x + 3 = 9x + 3
Since the left-hand side is exactly the same as the right hand side, then it has infinitely many solutions
3x + 2 = 7(x-2)
open the parenthesis
3x + 2 = 7x - 14
collect like term
7x -3x = 2 + 14
4x = 16
Divide both-side by 4
x = 4
It has exactly one solution
Using the following diagram below: Find the length of TT. Round youranswer to the nearest tenth.Note: The nearest tenth means you will round to one decimal place. YouMust Show Your Work.IPoints T, T', and 7" are shown.T"T'T
Answers
Let point T the origin
so
The coordinates of point T are (0,0)
therefore
The coordinates of point T' are (-2,1)
Find out the distance TT'
Applying the formula to calculate the distance between two points
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]substitute given coordinates
[tex]\begin{gathered} TT^{\prime}=\sqrt{(1-0)^2+(-2-0)^2} \\ TT^{\prime}=\sqrt{1^2+-2^2} \\ TT^{\prime}=\sqrt{5} \\ TT^{\prime}=2.2\text{ units} \end{gathered}[/tex]The answer is TT'=2.2 unitsWhat is an equation of the line that passes through the points (2, 2) and
(1, -2)
Answers
Answer: y = 4x + -6
Step-by-step explanation:
helppppppppppppppppppppppppppppppppppppppppp asapppppppppppppppppppppppppppppppp
Answers
Answer:
5
Step-by-step explanation:
((12*3)-(3*1/3))/((4*3-5))=
((36)-(1))/((12-5))=
(35)/(7)=5
Answer: it is going to be 35/7 = 5