Questions: Which graph represents the inequality? y ≤ (1/3)x - 1

Which graph represents the inequality? y ≤ (1/3)x - 1
Transcript text: Checkpoint 2 - Part 1 Which graph represents the inequality? \[ y \leq \frac{1}{3} x-1 \]
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Solution

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Solution Steps

Step 1: Identify the slope and y-intercept.

The inequality is given in slope-intercept form: y ≤ (1/3)x - 1. The slope is 1/3, and the y-intercept is -1.

Step 2: Determine the correct line.

We are looking for a line that crosses the y-axis at -1 and has a slope of 1/3 (rises 1 unit for every 3 units it moves to the right). The top two graphs have lines with these properties. The bottom two graphs have incorrect y-intercepts.

Step 3: Determine the correct shading.

The inequality symbol is "less than or equal to." This means the area below the line should be shaded, and the line itself should be solid. The top left graph has these properties. The top right graph has the area above the line shaded.

Final Answer:

The top-left graph represents the inequality.

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