Question

How do you write `-3x+2y=7` in slope-intercept form? What is the slope and `y`-intercept?

Answer 1

See a solution process below:

Explanation:

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.

First, add `color(red)(3x)` to each side of the equation:

`color(red)(3x) - 3x + 2y = color(red)(3x) + 7`

`0 + 2y = 3x + 7`

`2y = 3x + 7`

Now, divide each side of the equation by `color(red)(2)`:

`(2y)/color(red)(2) = (3x + 7)/color(red)(2)`

`(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = (3x)/color(red)(2) + 7/color(red)(2)`

`y = color(red)(3/2)x + color(blue)(7/2)`

Therefore:

• The slope is: `color(red)(m = 3/2)`

• The `y`-intercept is: `color(blue)(b = 7/2)` or `(0, color(blue)(7/2))`