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Question 1159298: Write the equation of the line that passes through the points open parentheses negative 1 comma space minus 11 close parentheses and open parentheses negative 2 comma space minus 15 close parentheses. Write your answer in slope-intercept form.
Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! -------------------------------------------------------
open parentheses negative 1 comma space minus 11 close parentheses and open parentheses negative 2 comma space minus 15 close parentheses.
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(-1, -11), and (-2, -15)
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Problem
Write the equation of the line that passes through the points (-1, -11) and (-2, -15). Write your answer in slope-intercept form.
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Answer: y = 4x - 7
slope = 4, y intercept = -7
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Work Shown:
Find the slope of the line through (x1,y1) = (-1,-11) and (x2,y2) = (-2,-15)
m = (y2 - y1)/(x2 - x1)
m = (-15 - (-11))/(-2 - (-1))
m = (-15 + 11)/(-2 + 1)
m = (-4)/(-1)
m = 4
The slope is 4, which is the same as 4/1, meaning we have a rise of 4 and a run of 1.
Plug m = 4 and (x1,y1) = (-1,-11) into the point slope formula. Solve for y.
y - y1 = m(x - x1)
y - (-11) = 4(x - (-1)) ... replace m with 4, x1 with -1, and y1 with -11
y + 11 = 4(x + 1) ... subtracting a negative is the same as adding
y + 11 = 4*x + 4*(1) ... distributive property
y + 11 = 4x + 4
y + 11 - 11 = 4x + 4 - 11 .... subtract 11 from both sides
y = 4x - 7 ... combine like terms
This is in the form y = mx+b with m = 4 as the slope and b = -7 as the y intercept
The y intercept as an ordered pair is (0, -7)
To confirm that y = 4x-7 is the correct answer, let's plug in x = -1 and see what happens
y = 4x-7
y = 4(-1) - 7
y = -4 - 7
y = -11
Therefore, x = -1 and y = -11 pair up to get us the point (-1, -11)
Repeat for x = -2
y = 4x-7
y = 4(-2) - 7
y = -8-7
y = -15
Leading to the point (-2,-15)
So we have confirmed y = 4x-7 as the proper answer as it goes through (-1, -11) and (-2,-15) as the instructions require.
Extra info: the x intercept is x = 7/4 = 1.75 which is found by plugging in y = 0 and solving for x. So you would solve 0 = 4x-7 for x.
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