Question

Which following system of inequalities describes the graph below?

Answer 1

A system of inequalities that describes the graph include the following;

y ≤ 2x + 5

y > x - 1

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

`y - y_1 = m(x - x_1)`

Where:

• x and y represent the data points.
• m represent the slope.

First of all, we would determine the slope for the solid line by using these points (2, 1) and (0, 5);

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

Slope (m) = (5 - 1)/(0 - 2)

Slope (m) = 2

At data point (0, 5) and a slope of 2, an inequality for this line can be calculated by using the point-slope form as follows:

`y - y_1 = m(x - x_1)`

y - 5 = 2(x - 0)

y = 2x + 5

y ≤ 2x + 5 (since the line is solid and shaded below).

For the dashed line, we have

Slope (m) = (-1 - 0)/(0 - 1)

Slope (m) = 1

At data point (0, -1) and a slope of 1, an inequality for this line can be calculated by using the point-slope form as follows:

`y - y_1 = m(x - x_1)`

y + 1 = (x - 0)

y = x - 1

y > x - 1 (since the line is dashed and shaded above).