Question

Find the inequality by the graphtwo variable inequalities from their graphs.

Answer 1

To find the inequality on the graph, first, we need to find the equation of the line.

The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

`m=(y_2-y_1)/(x_2-x_1)`

The line passes through (0, -2) and (2, -5), then its slope is:

`m=(-5-(-2))/(2-0)=-(3)/(2)`

From the graph, the y-intercept is -2. Then, using the slope-intercept form, the equation of the line is:

y = -3/2x - 2

Given that the line is solid and the shaded area is below the line, the inequality is:

y ≤ -3/2x - 2