Question

graph the inequality.
y > -3x + 5

Explanation:

Step1: Graph the boundary line

The inequality \( y > - 3x+5 \) has a boundary line \( y=-3x + 5 \). Using the slope - intercept form \( y = mx + b \), we identify the y - intercept \( b = 5 \) (so the point \( (0,5) \)) and the slope \( m=-3 \). We plot the y - intercept and use the slope to find a second point. Since the inequality is strict (\( > \)), we draw a dashed line.

Step2: Determine the shaded region

We use the test point \( (0,0) \). Substituting into the inequality gives a false statement, so we shade the region opposite to where \( (0,0) \) lies, which is above the dashed line.

Answer:

To graph \( y > -3x + 5 \):

1. Graph the boundary line: The equation \( y = -3x + 5 \) is in slope - intercept form (\( y=mx + b \)) where \( m=-3 \) (slope) and \( b = 5 \) (y - intercept). Plot the y - intercept at \( (0,5) \). Then, use the slope to find another point. Since the slope is \( - 3=\frac{-3}{1} \), from \( (0,5) \), move down 3 units and right 1 unit to get \( (1,2) \). Draw a dashed line (because the inequality is \( > \), not \( \geq \)) through these points.
2. Shade the region: To determine which side of the line to shade, pick a test point not on the line. A common test point is \( (0,0) \). Substitute \( x = 0 \) and \( y = 0 \) into the inequality \( y>-3x + 5 \): \( 0>-3(0)+5\) simplifies to \( 0 > 5 \), which is false. So we shade the region that does not contain \( (0,0) \), which is the region above the dashed line \( y=-3x + 5 \).