Question

What is the slope of the line represented by the equation 4x + 8y = 4?

Answer 1

The slope is `color(red)(m = -1/2)`

Explanation:

To find the slope we can transform this line 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.

Solving for `y` gives:

`4x + 8y = 4`

`color(red)(-4x) + 4x + 8y = color(red)(-4x) + 4`

`0 + 8y = color(red)(-4x) + 4`

`8y = -4x + 4`

`(8y)/color(red)(8) = (-4x + 4)/color(red)(8)`

`(color(red)(cancel(color(black)(8)))y)/cancel(color(red)(8)) = (-4x)/color(red)(8) + 4/color(red)(8)`

`y = color(red)(-1/2)x + color(blue)(1/2)`