SOLUTION: Question: Write an equation of the line that has each pair of intercepts. x-intercept:2, Y-intercept:-4 How do I do this?

Algebra ->  Linear-equations -> SOLUTION: Question: Write an equation of the line that has each pair of intercepts. x-intercept:2, Y-intercept:-4 How do I do this?      Log On


   

Question 175487: Question: Write an equation of the line that has each pair of intercepts.
x-intercept:2, Y-intercept:-4 How do I do this?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x-intercept:2 tells us that the point (2,0) is on the line
y-intercept: -4 means that (0,-4) is on the line


So we need to find the equation of the line through the points (2,0) and (0,-4)





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


m=%28-4%29%2F%280-2%29 Subtract 0 from -4 to get -4


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


m=2 Reduce


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


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-0=2%28x-2%29 Plug in m=2, x%5B1%5D=2, and y%5B1%5D=0


y-0=2x%2B2%28-2%29 Distribute


y-0=2x-4 Multiply


y=2x-4%2B0 Add 0 to both sides.


y=2x-4 Combine like terms.


y=2x-4 Simplify


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


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