Questions: Which of the following systems of inequalities matches the graph shown?

Solution Steps

The red shaded area corresponds to the first inequality. The line has a negative slope and a positive y-intercept. The shading is above the line, suggesting a "greater than or equal to" inequality. The line appears to pass through points (0,6) and (-1,14). This gives a slope of (14-6)/(-1-0) = -8. The y-intercept is 6. Thus, the equation of the line is y = -8x + 6. Since the shaded region is above the line, the inequality is y ≥ -8x + 6.

The blue shaded area corresponds to the second inequality. The line has a positive slope and a positive y-intercept. The shading is below the line, suggesting a "less than or equal to" inequality. The line appears to cross the y-axis near 2 and goes through the point (1,4). If this line passes through (0,2) and (1,4) the slope is (4-2)/(1-0)=2. The equation of the line would then be y = 2x+2. The shaded region is below the line so the inequality should be y ≤ 2x+2.

Combining our findings from the previous steps, the system of inequalities is:

y ≥ -8x + 6 y ≤ 2x + 2

Final Answer