Question

y < -x + 2
y < 4x - 3
a)

b)

c)

d)

Explanation:

Step1: Analyze the first inequality \( y < -x + 2 \)

The line \( y = -x + 2 \) has a slope of \(-1\) and a y - intercept of \( 2 \). Since the inequality is \( y < -x + 2 \), the line should be dashed (because of the strict inequality \( < \)) and the region below the line should be shaded.

Step2: Analyze the second inequality \( y < 4x - 3 \)

The line \( y = 4x - 3 \) has a slope of \( 4 \) and a y - intercept of \(-3\). Since the inequality is \( y < 4x - 3 \), the line should be dashed and the region below the line should be shaded.

Step3: Check the intersection of the shaded regions

We need to find the graph where both the region below \( y=-x + 2 \) (dashed line, slope - 1, y - intercept 2) and the region below \( y = 4x-3 \) (dashed line, slope 4, y - intercept - 3) are shaded.

• For option A: The shaded region does not match the regions below both lines.
• For option B: The shaded region does not match the regions below both lines.
• For option C: Let's check the lines. The line with slope - 1 ( \( y=-x + 2 \)) and slope 4 ( \( y = 4x-3 \)): The region below \( y=-x + 2 \) (dashed line) and below \( y = 4x-3 \) (dashed line) is correctly shaded.
• For option D: The lines and shaded regions do not match the given inequalities.

Answer:

C