Question

Y ≥ - 5/3x - 5 how do i graph this?

Answer 1

Refer to the step-by-step explanation and the attached image.

Explanation:

The main steps involved are graphing the boundary line, choosing the type of line (solid or dashed), and determining the region to shade.

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Graphing the Boundary Line
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To graph the inequality:

`y \geq -(5)/(3)x-5`

You'll start by graphing the line:

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

Steps on how to Graph a Line:

To graph a line in the form y = mx + b:

1. Plot 'b' on the y-axis as your starting point.

• In our case, 'b' is the point (0, -5)

2. From there, move 'm' units up (down if -m) and 1 unit right to mark a new point.

`\text{Recall that} \ m =\frac{\text{rise}}{\text{run}}`

• In our case move 5 units down (since 'm' is negative) and 3 units right

3. Connect the points with a straight line.

Optionally, you can plot more points using the slope for increased accuracy, and then draw the line through all the points.

This graphed line represents the boundry line.

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Determining the Type of Line:
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• If < or > then dashed line.
• If ≤ or ≥ than solid line.

In our case we have a solid line.

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Shading the Region
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1. Choose a test point that is not on the line to determine which side of the line to shade. A common choice is the origin (0,0), provided the line doesn't pass through it.

2. Substitute the coordinates of the test point into the inequality.

`\Longrightarrow 0 \geq -(5)/(3)(0)-5\\\\\\\\\therefore 0 \geq -5 \ \bold{True}`

3. Since the inequality holds, we shade the region that contains the test point.