Question

TIME REMAINING
09:44
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4). Everything to the right of the line is shaded.

Which linear inequality is represented by the graph?

y ≥ One-thirdx – 4
y ≤ One-thirdx – 4
y ≤ One-thirdx + 4
y ≥ One-thirdx + 4

Answer 1

Since everything to the right of the line is shaded, the linear inequality which represents the graph is equal to: A. y ≥ 1/3x - 4.

How to determine the linear inequality?

In order to determine the linear inequality which represents the graph, we would find the slope of the given points.

Mathematically, the slope of a straight line can be calculated by using this formula;

$Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}$

Substituting the given points into the formula, we have;

$Slope = \frac{-4\;-\;(-5)}{0\;-\;(-3)}\\\\Slope = \frac{1}{3}$

Slope = 1/3.

From the standard equation, we have:

y - y₁ = m(x - x₁)

y - (-5) = 1/3(x - (-3))

y + 5 = 1/3x + 1

y = 1/3x + 1 - 5

y = 1/3x - 4

y ≥ 1/3x - 4.

Read more on slope here: brainly.com/question/3493733

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