SOLUTION: write the equation of the line which contains (-3,1) and whose y intercept is -8

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Question 118749: write the equation of the line which contains (-3,1) and whose y intercept is -8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the y-intercept is -8, then the line goes through the point (0,-8)


First lets find the slope through the points (-3,1) and (0,-8)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (-3,1) and is the second point (0,-8))

m=%28-8-1%29%2F%280--3%29 Plug in y%5B2%5D=-8,y%5B1%5D=1,x%5B2%5D=0,x%5B1%5D=-3 (these are the coordinates of given points)

m=+-9%2F3 Subtract the terms in the numerator -8-1 to get -9. Subtract the terms in the denominator 0--3 to get 3


m=-3 Reduce

So the slope is
m=-3

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-1=%28-3%29%28x--3%29 Plug in m=-3, x%5B1%5D=-3, and y%5B1%5D=1 (these values are given)


y-1=%28-3%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-1=-3x%2B%28-3%29%283%29 Distribute -3

y-1=-3x-9 Multiply -3 and 3 to get -9

y=-3x-9%2B1 Add 1 to both sides to isolate y

y=-3x-8 Combine like terms -9 and 1 to get -8
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Answer:


So the equation of the line which goes through the points (-3,1) and (0,-8) is:y=-3x-8

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-3 and the y-intercept is b=-8

Notice if we graph the equation y=-3x-8 and plot the points (-3,1) and (0,-8), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=-3x-8 through the points (-3,1) and (0,-8)

Notice how the two points lie on the line. This graphically verifies our answer.