Question

Which graph shows the inequality y < –2x + 3?

Answer 1

Your line should be dashed and the shading (solution area) should be below your line.

Your line should cross the y-axis at 3.
From there, count 2 spaces down, then 1 space to the right. Place a point. Repeat.

Answer 2

Below diagram shows the y < –2x + 3 graph.

Graph the Line

y=−2x+3:

Find the y-intercept: When

x=0,

y=3. So, the y-intercept is (0, 3).

Find the x-intercept: When

y=0,

−2x+3=0, solving for

x gives

x = 3/2 . So, the x-intercept is

( 3/2 ,0 )

Plot these points and draw a straight line through them.

Shade the Region Below the Line:

Since the inequality is

y<−2x+3, we want the region below the line.

Choose a test point not on the line. The origin (0,0) is a convenient choice.

Substitute the coordinates of the test point into the inequality. If it is true, shade the region containing the test point; otherwise, shade the other region.

For the origin,

0<3, which is true. So, shade the region below the line.

Remember, the line itself is not included because of the strict inequality (

< <).

If you have access to graphing software or tools, you can input the equation

y=−2x+3 and then manually shade the region below the line. Alternatively, you can use online graphing calculators to visualize this.