Question

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

Answer 1

See the explanation below.

Explanation:

Graph:

`y-2=2/3(x-4)`

The easiest way to find points on the line is to convert the given equation in point slope form to slope intercept form: `y=mx+b`, where `m` is the slope, and `b` is the y-intercept. In order to do this, solve the point slope equation for `y`.

`y-2=2/3(x-4)`

Add `2` to both sides.

`y=2/3(x-4)+2`

Simplify `2/3(x-4)` to `(2(x-4))/3`.

`y=(2(x-4))/3+2`

Expand.

`y=(2x)/3-8/3+2`

Simplify.

`y=2/3x-8/3+2`

Multiply `2` by `3/3` to get the same denominator as `-8/3`.

`y=2/3x-8/3+2xx3/3`

Simplify.

`y=2/3x-8/3-6/3`

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

Determine two or three points on the line by choosing values for `x` and solving for `y`.

`"Points"`

`x=-2,` `y=-2`

`x=0,` `y=-2/3`

`x=1,` `y=0`

Plot the points and draw a straight line through them.

graph{y=2/3(x-4)+2 [-12.66, 12.65, -6.33, 6.33]}