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=\frac{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

$0=\frac{5}{7}x+10,$

so let's do so:

$-10=\frac{5}{7}x$$-70=5x$$-14=x$

So, the x-intercept will be

$(-14,0)$