Question

Find the x- and y-intercepts of 5x−7y=−70.(Enter each intercept in the form (a,b).)

Answer 1

Let's first write the equation in its slope intercept form, as that will make it easier to work with it.

`5x-7y=-70`
`-7y=-5x-70`
`7y=5x+70`
`y=(5)/(7)x+10`

This immedately tells us that the line will intercept the y-axis at y=10, so the y-intercept will be

`(0,10)`

Now, in order to determine the x-intercept, we must solve the equation

`0=(5)/(7)x+10,`

so let's do so:

`-10=(5)/(7)x`
`-70=5x`
`-14=x`

So, the x-intercept will be

`(-14,0)`