SOLUTION: Find an equation in slope-intercept form for the line that passes through (-3,1)and (-2,-3).

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Question 174831This question is from textbook
: Find an equation in slope-intercept form for the line that passes through (-3,1)and (-2,-3).This question is from textbook

Found 2 solutions by jim_thompson5910, nerdybill:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-3-1%29%2F%28-2--3%29 Plug in y%5B2%5D=-3, y%5B1%5D=1, x%5B2%5D=-2, and x%5B1%5D=-3


m=%28-4%29%2F%28-2--3%29 Subtract 1 from -3 to get -4


m=%28-4%29%2F%281%29 Subtract -3 from -2 to get 1


m=-4 Reduce


So the slope of the line that goes through the points and is m=-4


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-1=-4%28x--3%29 Plug in m=-4, x%5B1%5D=-3, and y%5B1%5D=1


y-1=-4%28x%2B3%29 Rewrite x--3 as x%2B3


y-1=-4x%2B-4%283%29 Distribute


y-1=-4x-12 Multiply


y=-4x-12%2B1 Add 1 to both sides.


y=-4x-11 Combine like terms.


y=-4x-11 Simplify


So the equation that goes through the points and is y=-4x-11


Notice how the graph of y=-4x-11 goes through the points and . So this visually verifies our answer.
drawing%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-4x-11%29%2C%0D%0A+circle%28-3%2C1%2C0.08%29%2C%0D%0A+circle%28-3%2C1%2C0.10%29%2C%0D%0A+circle%28-3%2C1%2C0.12%29%2C%0D%0A+circle%28-2%2C-3%2C0.08%29%2C%0D%0A+circle%28-2%2C-3%2C0.10%29%2C%0D%0A+circle%28-2%2C-3%2C0.12%29%0D%0A+%29 Graph of y=-4x-11 through the points and

Answer by nerdybill(5407) About Me  (Show Source):
You can put this solution on YOUR website!
Slope of a line between two points is:
m = (y2-y1)/(x2-x1)
.
So, the two given in your problem is:
(-3,1)and (-2,-3)
plugging it in we get:
m = (-3-1)/(-2-(-3))
m = (-4)/(-2+3)
m = (-4)/(1)
m = -4
.
Now, using the "point slope" form of an equation:
y - y1 = m(x-x1)
Using one of the two points provided along with the calculated slope:
y - 1 = -4(x-(-3))
y - 1 = -4(x+3)
y - 1 = -4x - 12
y = -4x - 11 (this is what they're looking for)