Question

What is the slope and intercept of `x+9y=5`?

Answer 1

The slope is `color(red)(m = -1/9)`

The y-intercept is `color(blue)(b = 5/9)`

Explanation:

To find the slope and intercept of this equation it must be in 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.

Solving for `y` gives:

`x - color(red)(x) + 9y = - color(red)(x) + 5`

`0 + 9y = -x + 5`

`9y = -x + 5`

`(9y)/color(red)(9) = (-x + 5)/color(red)(9)`

`(color(red)(cancel(color(black)(9)))y)/cancel(color(red)(9)) = -x/9 + 5/9`

`y = color(red)(-1/9)x + color(blue)(5/9)`

The slope is `color(red)(m = -1/9)`

The y-intercept is `color(blue)(b = 5/9)`