Question

How do you find the slope given `x + 2y=3`?

Answer 1

Convert the equation to the slope-intercept form - see entire explanation below:

Explanation:

To find the slope we need to convert the 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 + 2y = 3`

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

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

`0 + 2y = -x + 3`

`2y = -x + 3`

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

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

`y = -1/2x + 3/2`

With the equation now in slope intercept form we can see the slope is `color(red)(m = -1/2)`