QuestionGraph the inequality.
Studdy Solution
STEP 1
1. We are graphing a linear inequality in two variables, and .
2. The inequality represents a region on the coordinate plane.
3. The boundary of this region is the line .
STEP 2
1. Graph the boundary line .
2. Determine the region that satisfies the inequality .
STEP 3
Graph the boundary line .
- Find the y-intercept by setting :
$ y = -4(0) - 5 = -5
\]
So, the y-intercept is \((0, -5)\).
- Find another point by choosing a value for , for example, :
$ y = -4(1) - 5 = -9
\]
So, another point on the line is \((1, -9)\).
- Plot the points and on the coordinate plane.
- Draw a solid line through these points because the inequality is , indicating that points on the line are included in the solution set.
STEP 4
Determine the region that satisfies the inequality .
- Choose a test point not on the line to determine which side of the line to shade. A common test point is .
- Substitute into the inequality:
$ 0 \geq -4(0) - 5 \implies 0 \geq -5
\]
This is true, so the region that includes \((0, 0)\) satisfies the inequality.
- Shade the region above the line, which includes the line itself, to represent all the solutions to the inequality .
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