Question

How do you graph `-3y<21` on the coordinate plane?

Answer 1

See a solution process below:

Explanation:

Divide each side of the inequality by `color(blue)(-3)` to solve for `y` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`(-3y)/color(blue)(-3) color(red)(>) 21/color(blue)(-3)`

`(color(blue)(cancel(color(black)(-3)))y)/cancel(color(blue)(-3)) color(red)(>) -7`

`y > -7`

To graph this we will draw a horizontal at `-7` on the vertical axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade above the the line because the inequality operator does contain a "greater than" clause:

graph{y>=-7 [-15, 15, -12.5, 12.50]}