Question

How do you find the slope and intercept for `x+10y=7`?

Answer 1

Convert to slope-intercept form and pull the correct values from this form of the equation. See the full explanation below.

Explanation:

To find the slope and y-intercept we will transform this equation to the slope-intercept form by solving for `y`:

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.

`x + 10y = 7`

`x - color(green)(x) + 10y = - color(green)(x) + 7`

`0 + 10y = - color(green)(x) + 7`

`10y = - color(green)(x) + 7`

`(10y)/color(green)(10) = (-color(green)(x) + 7)/color(green)(10)`

`(color(green)(cancel(color(black)(10)))y)/cancel(color(green)(10)) = -1/10x + 7/10`

`y = color(red)(-1/10)x + color(blue)(7/10)`

The slope is `m = color(red)(-1/10)`

The y-intercept is `b = color(blue)(7/10)`