SOLUTION: What is the slope-intercept equation for the line below? (4,1) (0,-4)

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: What is the slope-intercept equation for the line below? (4,1) (0,-4)      Log On


   

Question 274981: What is the slope-intercept equation for the line below?
(4,1)
(0,-4)
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=4 and y%5B1%5D=1.
Also, is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=-4.


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


m=%28-4-1%29%2F%280-4%29 Plug in y%5B2%5D=-4, y%5B1%5D=1, x%5B2%5D=0, and x%5B1%5D=4


m=%28-5%29%2F%280-4%29 Subtract 1 from -4 to get -5


m=%28-5%29%2F%28-4%29 Subtract 4 from 0 to get -4


m=5%2F4 Reduce


So the slope of the line that goes through the points and is m=5%2F4


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=%285%2F4%29%28x-4%29 Plug in m=5%2F4, x%5B1%5D=4, and y%5B1%5D=1


y-1=%285%2F4%29x%2B%285%2F4%29%28-4%29 Distribute


y-1=%285%2F4%29x-5 Multiply


y=%285%2F4%29x-5%2B1 Add 1 to both sides.


y=%285%2F4%29x-4 Combine like terms.


y=%285%2F4%29x-4 Simplify


So the equation that goes through the points and is y=%285%2F4%29x-4


Notice how the graph of y=%285%2F4%29x-4 goes through the points and . So this visually verifies our answer.
Graph of y=%285%2F4%29x-4 through the points and