Question

Find the y intercept and x intercept of the linear equation 7/8x-5y=-3

Answer 1

Answer: y =
`(3)/(5)` and x =
`(-24)/(7)`

Explanation:

The y-intercept of a line is the point where the line hits (or intercepts) the y-axis. You could also think of it as the value of y when x = 0; to find the y-intercept, take your given equation and plug in 0 for x and solve for y.

`(7)/(8)`x - 5y = -3 original equation

`(7)/(8)`(0) - 5y = -3 plug 0 in for x

0 - 5y = -3 any number multiplied by 0 = 0

-5y = -3

`(-5y)/(-5)` =
`(-3)/(-5)` divide both sides by -5 to get y by itself

y =
`(3)/(5)` solved for y

So, our y-intercept is
`(3)/(5)`.

The x-intercept of a line is the point where the line hits (or intercepts) the x-axis. You could also think of it as the value of x when y = 0; to find the x-intercept, take your given equation and plug in 0 for y and solve for x.

`(7)/(8)`x - 5y = -3 original equation

`(7)/(8)`x - 5(0) = -3 plug 0 in for y

`(7)/(8)`x - 0 = -3 any number multiplied by 0 = 0

`(7)/(8)`x = -3

`(8)/(7)` *
`(7)/(8)`x = -3 *
`(8)/(7)` multiply both sides by
`(8)/(7)` to get x by itself

x =
`(-24)/(7)` solved for x

So, our x-intercept is
`(-24)/(7)`.

Side note: since the number attached to x is a fraction, in order to get x by itself, you multiply both sides of the equation by the reciprocal of the fraction, so the numerator and denominator swap places.

I hope this helped! :)