ACT Math : How to graph a two-step inequality

Study concepts, example questions & explanations for ACT Math

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Example Questions

例子问题# 191:Coordinate Plane

Solve and graph the following inequality:

Possible Answers:

Correct answer:

Explanation:

To solve the inequality, the first step is to addto both sides:

The second step is to divide both sides by:

To graph the inequality, you draw a straight number line. Fill in the numbers fromto infinity. Infinity can be designated by a ray. Be sure to fill in the number, since the equation indicated greater than ORequal to.

The graph should look like:

Number_line

Example Question #2 :Graphing

Pointsandlie on a circle. Which of the following could be the equation of that circle?

Possible Answers:

Correct answer:

Explanation:

If we plug the pointsandinto each equation, we find that these points work only in the equation. This circle has a radius ofand is centered at.

Example Question #3 :Graphing

Which of the following lines is perpendicular to the line?

Possible Answers:

Correct answer:

Explanation:

The key here is to look for the line whose slope is the negative reciprocal of the original slope.

In this case,is the negative reciprocal of.

Therefore, the equation of the line which is perpendicular to the original equation is:

Example Question #1 :How To Graph A Two Step Inequality

LetDbe the region on the (x,y) coordinate plane that contains the solutions to the following inequalities:

, whereis a positive constant

Which of the following expressions, in terms of, is equivalent to the area ofD?

Possible Answers:

Correct answer:

Explanation:

Inequality_region1

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