Question

pretest: systems of linear equations and inequalities
a. $y < 2x - 3$
$y < \frac{1}{3}x + 4$
b. $y > 2x - 3$
$y > \frac{1}{3}x + 4$
c. $y > 2x - 3$
$y < \frac{1}{3}x + 4$
d. $y < 2x - 3$
$y > \frac{1}{3}x + 4$

Explanation:

Step1: Analyze the line \( y = 2x - 3 \)

The line \( y = 2x - 3 \) has a slope of \( 2 \) and a y - intercept of \( - 3 \). The shaded region is above this line (since the line is dashed, the inequality is strict). So the inequality for this line is \( y>2x - 3 \).

Step2: Analyze the line \( y=\frac{1}{3}x + 4 \)

The line \( y=\frac{1}{3}x + 4 \) has a slope of \( \frac{1}{3} \) and a y - intercept of \( 4 \). The shaded region is below this line (since the line is dashed, the inequality is strict). So the inequality for this line is \( y<\frac{1}{3}x + 4 \).

Answer:

C. \( y > 2x - 3 \)
\( y < \frac{1}{3}x + 4 \)