Skip to main content
Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 35
Chapter 6, Problem 35

Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

Verified step by step guidance
1
Identify the inequality given: \(y \leq -3x - 6\). This represents all points on or below the line \(y = -3x - 6\).
Rewrite the boundary line equation: \(y = -3x - 6\). This line has a slope of \(-3\) and a y-intercept at \(-6\).
Determine the shading region for the inequality \(y \leq -3x - 6\). Since it is \(\leq\), the solution includes the line and the area below it.
On each graph option (A–D), look for the line with slope \(-3\) and y-intercept \(-6\), then check which graph shades the region below this line.
Match the inequality \(y \leq -3x - 6\) to the graph that shows the line \(y = -3x - 6\) with shading below or on the line.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Graphing Linear Inequalities

Graphing a linear inequality involves first graphing the related linear equation as a boundary line. The inequality symbol determines whether the boundary is solid (≤ or ≥) or dashed (< or >). The solution region is the half-plane where the inequality holds true, shaded accordingly.
Recommended video:
06:07
Linear Inequalities

Slope-Intercept Form

The slope-intercept form y = mx + b expresses a line with slope m and y-intercept b. For y ≤ -3x - 6, the slope is -3, indicating the line falls steeply, and the y-intercept is -6, where the line crosses the y-axis. This form helps quickly sketch the boundary line.
Recommended video:
Guided course
03:56
Slope-Intercept Form

Testing Points to Determine Shading

To identify which side of the boundary line to shade, select a test point not on the line (often (0,0)) and substitute into the inequality. If the inequality is true, shade the region containing that point; if false, shade the opposite side. This confirms the correct solution region.
Recommended video:
Guided course
4:36
Determinants of 2×2 Matrices
Related Practice
Textbook Question

Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary.

5x - 5y - 3 = 0

x - y - 12 = 0

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

5x2−2y2=255x^2 - 2y^2 = 25

10x2+y2=5010x^2 + y^2 = 50

5
views
Textbook Question

Find each sum or difference, if possible.

[−43]−[582]\(\left\)[ \(\begin{matrix}\) -4 & 3 \(\end{matrix}\) \(\right\)] - \(\left\)[ \(\begin{matrix}\) 5 & 8 & 2 \(\end{matrix}\) \(\right\)]

Textbook Question

Evaluate each determinant.

∣−1829∣\(\left\)| \(\begin{matrix}\) -1 & 8 \\ 2 & 9 \(\end{matrix}\) \(\right\)|

Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (-x4 - 8x2 + 3x - 10)/((x + 2)(x2 + 4)2)

Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (x2)/(x4 - 1)