Question

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

Answer 1

Graph and solve `y < (3x)/2 - 3`

Explanation:

`y < (3x)/2 - 3 (1)`
First graph the line `y = (3x)/2 - 3` by its intercepts.
Make x = 0 --> y = -3. Make y = 0 --> x = 2.
Next, solve the inequality (1). The solution set area is below the line
y. Color it. It is the answer.
graph{(3x)/2 - 3 [-10, 10, -5, 5]}

Answer 2

The slope is `3/2`.
The y-intercept is `-3`.
The x-intercept is `2`.

Explanation:

`y<3/2x-3` is in the slope-intercept form `y=mx+b`, where `m` is the slope, and `b` is the y-intercept. The slope of the line for `y<3/2x-3` is `3/2`, and the y-intercept is `-3`.

Determine two points on the line by substituting values for `x` then solving for `y`.

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

Plot the points. Draw a straight dashed line through the points to indicate that the line is the boundary of the inequality, but is not included in the inequality. Shade in the area below the line.

graph{y<3/2x-3 [-10.17, 9.83, -6.24, 3.76]}