Question

Write the inequality represented by the graph below.

Answer 1

Answer:

y > 3x - 1

Step-by-step explanation:

To find out what the linear inequality of the graph:

We need to determine its slope and y-intercept. Given the following points on the graph: (1, 2) and (0, -1)

Let (x1,  y1) = (1, 2)

(x2, y2) = (0, -1)

To solve for slope, we'll use the formula:

$m = \frac{y2 - y1}{x2 - x1}$

$m = \frac{y2 - y1}{x2 - x1} = \frac{-1 - 2}{0 - 1} = \frac{-3}{-1} = 3$

Therefore, the slope = 3.

Next, we must determine the y-intercept of the line. The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates (0, b). One of the points we used to solve for the slope reflects the coordinates of the y-intercept, (0, -1). Therefore, the y-intercept (b) =  -1.

Now that we have our slope and y-intercept, we can establish the linear equation in slope-intecept form:

y = 3x - 1.

Since the upper half of the region is already shaded, then it means that the inequality symbol must be ">". Therefore, the linear inequality of the graph is y > 3x - 1.

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