Question

Listen Write a system of linear inequalities represented by the graph.

Inequality 1:
Inequality 2:
​

Answer 1

A system of linear inequalities represented by the graph include:

Inequality 1: y ≥ -3/4(x) + 2

Inequality 2: y ≤ 2x - 3.

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 of the downward sloping line by using these points (4, -1) and (0, 2);

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

Slope (m) = (2 + 1)/(0 - 4)

Slope (m) = -3/4

At data point (0, 2) and a slope of -3/4, an equation for this line can be calculated by using the point-slope form as follows:

y - 2 = -3/4(x - 0)

y = -3/4(x) + 2

y ≥ -3/4(x) + 2 (since the solid line is shaded above)

For the the slope of the upward sloping line, we have;

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

Slope (m) = (1 - 3)/(2 - 3)

Slope (m) = 2/1 = 2

At data point (2, 1) and a slope of 2, an equation for this line can be calculated by using the point-slope form as follows:

y - 1 = 2(x - 2)

y = 2x - 3

y ≤ 2x - 3 (since the solid line is shaded below)