Question

Rewrite in a slope-intercept form and graph ​

Answer 1

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

Explanation:

Take the given equation:

`-3x+2y=6`

Solve for y so that the equation is written in slope-intercept form:

`y=mx+b`

m is the slope and b is the y-intercept. x and y are the coordinate points (x,y).

Solve for y:

Add 3x to both sides of the equation:

`-3x+3x+2y=6+3x\\\\2y=3x+6`

Divide both sides of the equation by 2 to isolate y:

`(2y)/(2)=(3x+6)/(2) \\\\ y=(3)/(2)x+3`

The slope is
`(3)/(2)` and the y-intercept is 3.

To graph, you need two points. You can use the y-intercept as one.

The y-intercept is the place where the line crosses over the y-axis, where x equals 0, so the point is (0,3).

Next, take any value for x and insert it into the equation. We'll use 2:

`y=(3)/(2)(2)+3`

Using this, you can solve for the value of y when x is equal to 2.

Simplify:

`(3)/(2) *(2)/(1)=(6)/(2)=3 \\\\y=3+3\\\\y=6`

So, when x=2, y is 6 (2,6).

Plot the points (0,3) and (2,6)

Draw a straight line through the two, going past both.

:Done

In the graph, one square is 1 unit