Question

How do you find the slope and y-intercept for the graph of the equation: 9x - 3y = 81?

Answer 1

graph{y = 3x - 27 [-5, 10, -30, 5]}

The slope is `color(red)(3)` and the y-intercept is `color(blue)(-27)` or (`color(blue)(0, -27)`)

Explanation:

To find the slope and y-intercept of this equation we must transform it into the slope-intercept form.

The slope-intercept form of a linear equation is:

`y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b` is the y-intercept value.

We can solve this equation for `y` to transform the equation we have been given in this problem into this form:

`9x - 3y = 81`

`9x - color(red)(9x) - 3y = color(red)(-9x) + 81`

`0 - 3y = color(red)(-9x) + 81`

`-3y = - color(red)(-9x) + 81`

`(-3y)/color(green)(-3) = (color(red)(-9x) + 81)/color(green)(-3)`

`(color(green)(cancel(color(black)(-3)))y)/cancel(color(green)(-3)) = (color(red)(-9x) + 81)/color(green)(-3)`

`y = (color(red)(-9x) + 81)/color(green)(-3)`

`y = color(red)(-9x)/color(green)(-3) + 81/color(green)(-3)`

`y = 3x - 27`

Therefore the slope is `color(red)(3)` and the y-intercept is `color(blue)(-27)` or (`color(blue)(0, -27)`)