On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which is the graph of the linear inequality y < 3x + 1?

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.

Question

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Answer :

MrRoyalgo MrRoyalgo · Answer 1

The attached graph represents the graph of the inequality

The points on the line are given as:

(-3,-7) and (0,2)

Start by calculating the linear equation using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]

This gives

[tex]y = \frac{2 + 7}{0 + 3}(x -0) + 2[/tex]

Evaluate the fraction expression

y = 3(x -0) + 2

Evaluate the difference

y = 3x + 2

From the question, we understand that the line of the inequality is a dashed line and the left of the line is shaded.

This means that the inequality is greater than i.e. >

So, we have:

y > 3x + 2

See attachment for the graph of the inequality