Question

Find an equation of a line with the x- and y-intercepts below. Use exact fractions when necessary.

x-intercept 7; y-intercept -5

Answer 1

`y=(5)/(7)x-5`

Explanation:

All lines in the plane are of the form

y = mx+b

The intersection with the Y-axis is obtained by replacing x with 0

The intersection with the X-axis is obtained by replacing y with 0

If we want that the Y-intercept = -5, then

-5 = m(0)+b

So b = -5

Our temporal equation is then

y = mx-5

If we want that the X-intercept = 7, then

0 = m(7)-5

7m = 5

m = 5/7

So our final equation is

`y=(5)/(7)x-5`

Attached is the graph of the line