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:
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{-1 - 2}{0 - 1} = \frac{-3}{-1} = 3[/tex]
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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