Write a system of linear inequalities that describes the shaded region.

Question

Quizplus · Accepted Answer

The shaded region appears to be a triangle with the base on the x-axis and one side passing through the point (4,6).

The equation for the base of the triangle along the x-axis is x ≤ 4.

The equation for the side passing through (4,6) can be found using the point-slope form of a line:
y - 6 = m(x - 4)

To find the slope, we can use another point on the line, let's say (2,2):
m = (6 - 2) / (4 - 2) = 2

Substituting m in the equation results in:
y - 6 = 2(x - 4)

Simplifying the equation gives us:
y ≤ -2x + 14

Thus, the system of inequalities that describes the shaded region is:
x ≤ 4
y ≤ -2x + 14

Write a System of Linear Inequalities That Describes the Shaded