Question

How do you graph `y=2/3x-4`?

Answer 1

Refer to the explanation.

Explanation:

Graph:

`y=2/3x-4` is the slope-intercept form of a linear equation:

`y=mx+b,`

where:

`m` is the slope and `b` is the y-intercept.

You need two points on the line. Let one of the points be the x-intercept and the other point be the y-intercept.

The y-intercept is `-4` (from the equation), which is the value of `y` when `x=0`. So the point is `(0,-4)`.

The x-intercept is the value of `x` when `y=0`.

To determine the x-intercept, substitute `0` for `y` and solve for `x`.

`0=2/3x-4`

Multiply both sides by `3`.

`3xx0=color(red)cancel(color(black)(3))^1xx2/color(red)cancel(color(black)(3))^1x-4xx3`

Simplify.

`0=2x-12`

Add `12` to both sides.

`12=2x`

Divide both sides by `2`.

`color(red)cancel(color(black)(12))^6/color(red)cancel(color(black)(2))^1=(color(red)cancel(color(black)(2))^1x)/color(red)cancel(color(black)(2))^1`

Simplify.

`6=x`

`x=6`

The x-intercept is `(6,0)`.

Plot the x- and y-intercepts and draw a straight line through them.

graph{y=2/3x-4 [-10, 10, -5, 5]}