SOLUTION: what is the equation of a line in slope intercept form that goes through(1,-1) and (-1,7)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: what is the equation of a line in slope intercept form that goes through(1,-1) and (-1,7)      Log On


   

Question 525846: what is the equation of a line in slope intercept form that goes through(1,-1) and (-1,7)
Answer by jim_thompson5910(35256) 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


Note: is the first point . So this means that x%5B1%5D=1 and y%5B1%5D=-1.
Also, is the second point . So this means that x%5B2%5D=-1 and y%5B2%5D=7.


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


m=%287--1%29%2F%28-1-1%29 Plug in y%5B2%5D=7, y%5B1%5D=-1, x%5B2%5D=-1, and x%5B1%5D=1


m=%288%29%2F%28-1-1%29 Subtract -1 from 7 to get 8


m=%288%29%2F%28-2%29 Subtract 1 from -1 to get -2


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


y%2B1=-4%28x-1%29 Rewrite y--1 as y%2B1


y%2B1=-4x%2B-4%28-1%29 Distribute


y%2B1=-4x%2B4 Multiply


y=-4x%2B4-1 Subtract 1 from both sides.


y=-4x%2B3 Combine like terms.


So the equation that goes through the points and is y=-4x%2B3


Notice how the graph of y=-4x%2B3 goes through the points and . So this visually verifies our answer.
Graph of y=-4x%2B3 through the points and