Math Practice Problems - Graphs to Linear Inequalities

Graphs to Linear Inequalities - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=1, Mode=simple

Write the inequality that represents this graph. Examples: y>3x/4, x<=2, y>=1, y>-2x

#	Problem	Correct Answer	Your Answer
1		Inequality:
Solution Vertical lines have undefined slope, and are expressed in the form x=[x-intercept]. The shaded region is to the right of the line, so we use a greater than sign. The line is dashed, so use > for greater than. x > ^-3

#	Problem	Correct Answer	Your Answer
2		Inequality:
Solution Horizontal lines have a slope of 0, and are expressed in the form y=[y-intercept] The shaded region is above the line, so we use a greater than sign. The line is dashed, so use > for greater than. y > ^-4

Complexity=1, Mode=y=mx+b

Write the inequality in y=mx+b format. Examples: y>2x-3, y<=-4x/3+1

Problem

Correct Answer

Your Answer

Inequality:

Solution
The slope is -¹/₄
The y intercept is -5
The shaded region is below the line, so we use a less than sign.
The line is solid, so use <= for less than or equal to.
Plugging this into y=mx+b results in

Problem

Correct Answer

Your Answer

Inequality:

Solution
The slope is ¹/₅
The y intercept is 5
The shaded region is below the line, so we use a less than sign.
The line is solid, so use <= for less than or equal to.
Plugging this into y=mx+b results in

Complexity=2, Mode=y=mx+b

Write the inequality in y=mx+b format. Examples: y>2x-3, y<=-4x/3+1

Problem

Correct Answer

Your Answer

Inequality:

Solution
The slope is ⁴/₅
The y intercept is 1
The shaded region is below the line, so we use a less than sign.
The line is solid, so use <= for less than or equal to.
Plugging this into y=mx+b results in

Problem

Correct Answer

Your Answer

Inequality:

Solution
The slope is ³/₅
The y intercept is 4
The shaded region is above the line, so we use a greater than sign.
The line is dashed, so use > for greater than.
Plugging this into y=mx+b results in

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