Question

Graph the solution set. $$ y<3 x-4 $$

   Graph the solution set.
$$
y<3 x-4
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 3, Problem 104

Instant Answer

Solved by Expert James Kiss

02/05/2022

Step 1

This line has a slope of 3 and a y-intercept of -4. We can plot the y-intercept at (0,-4) and then use the slope to find another point on the line. Since the slope is 3, we can go up 3 units and to the right 1 unit from the y-intercept to find another point at Show more…

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Graph the solution set. $$ y<3 x-4 $$

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Key Concepts

Shading the Region

Shading the region on the graph visually indicates all the points that satisfy the inequality. Once the boundary line is drawn, the correct half-plane is shaded, representing the entire solution set of the inequality.

Linear Inequality

A linear inequality involves a linear expression and an inequality sign (such as <, ?, >, or ?) indicating a relationship where one expression is smaller or larger than the other. In two variables, it describes a region in the coordinate plane, rather than a single line or a point.

Boundary Line

The boundary line is found by converting the inequality into an equality. This line acts as the divider between the solution region and the rest of the coordinate plane. For strict inequalities (such as < or >), the boundary is drawn as a dashed line to show that points on the line are not part of the solution set.

Graphing Linear Inequalities

Graphing linear inequalities involves plotting the appropriate boundary line and then determining which side of the line represents the set of points that satisfy the inequality. This process sometimes uses a test point to check inclusion in the solution set.

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