The two inequalities are:
a) y ≤ -2x + 5
b) y < 3x - 14
How to find the two graphed inequalities?
On the first graph, we can see that the shaded region is below the line and that the line is solid, so the inequality is of the form:
y ≤ line.
Now, remember that if the line passes through (x₁, y₁) and (x₂, y₂).
Then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
We can see that the line passes through (2, 1) and (-1, 3)
Then the slope is:
[tex]a = \frac{1 - 3}{2 - 1} = -2[/tex]
So the line is:
y = -2*x + b
To find the value of b, we use the point (2, 1), then we get:
1 = -2*2 + b
1 = -4 + b
1 + 4 = b = 5
Then the first inequality is:
y ≤ -2x + 5
Now let's go to the other line equation, again the shaded region is below the line and this time the line is dashed, then:
y < line.
Two points on the line are (5, 1) and (4, -2)
Then the slope is:
[tex]a = \frac{1 - (-2)}{5 - 4} = 3[/tex]
y = 3*x + b
To find the value of b, we use the point (5, 1)
Then:
1 = 3*5 + b
1 = 15 + b
1 - 15 = b = -14
Then the inequality is:
y < 3x - 14
If you want to learn more about inequalities:
https://brainly.com/question/18881247
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