Question

Graph the inequality on the axes below.
y, is greater than, minus, 3, x, minus, 8
y>−3x−8
x
y
x
y
Answer
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Answer 1

To graph the inequality \( y > -3x - 8 \):

1. **Graph the boundary line**: First, we will graph the equation \( y = -3x - 8 \). This is a straight line with a slope of -3 and a y-intercept of -8.

- Plot the y-intercept (0, -8).
- From (0, -8), use the slope to find another point. The slope of -3 means that for every 1 unit you go to the right (positive x-direction), you go down 3 units (negative y-direction). Starting from (0, -8), moving 1 unit right to (1, -8) takes you down to (1, -11).
- Connect these two points with a dashed line because the inequality is "greater than" and not "greater than or equal to."

2. **Determine the shading**: Since the inequality is \( y > -3x - 8 \), you will shade the area above the line, where the y-values are greater than the values on the line.

3. **Final graph**: You should have a dashed line for \( y = -3x - 8 \) and the region above this line shaded.

If you have access to graphing software or tools, you can sketch this out based on the steps above. If you're drawing it by hand, make sure to represent the dashed line correctly and shade appropriately.