Why can you use similar triangles to explain why the slope is the same between any two distinct points on a nonvertical line?(1 point)

Question

Responses

The hypotenuses of similar triangles used at different points along the line form the slope of the line. A ratio can be created from the hypotenuses of two similar triangles to calculate the slope of that line.
The hypotenuses of similar triangles used at different points along the line form the slope of the line. A ratio can be created from the hypotenuses of two similar triangles to calculate the slope of that line.

The interior angles of similar triangles used at different points along the line can be added to measure the slope of the line. The corresponding angles of similar triangles are the same, so the slope can be shown as the same using any two points along the line.
The interior angles of similar triangles used at different points along the line can be added to measure the slope of the line. The corresponding angles of similar triangles are the same, so the slope can be shown as the same using any two points along the line.

In similar triangles, the change in y
-values represents the run, and the change in x
-values represents the rise of the line the triangles are placed against. So the ratio riserun
can show that the slope is the same between any two points along the line.
In similar triangles, the change in y -values represents the run, and the change in x -values represents the rise of the line the triangles are placed against. So the ratio/rise over run End Fraction can show that the slope is the same between any two points along the line.

The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope. The corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line.
The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope. The corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line.
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Answer 1

The correct response is:

The legs of similar triangles used at different points along the line represent the rise and run of the line, or its slope. The corresponding sides of similar triangles are proportional, so the slope can be shown as the same using any two points along the line.

This explanation highlights how the proportionality of the sides of similar triangles demonstrates that the ratio of rise (change in y) to run (change in x) remains constant, illustrating that the slope is the same between any two distinct points on a nonvertical line.

Answer 2

Use the table to answer the question.

Time walking (minutes) 20 30 40 60 80
Calories burned 100 150 200 300 400
The table shows a relationship between the amount of time spent walking and the number of calories burned. Determine if the relationship is proportional.

(1 point)
Responses

The relationship is non-proportional; the graph does not pass through the origin.
The relationship is non-proportional; the graph does not pass through the origin.

The relationship is proportional.
The relationship is proportional.

The relationship is non-proportional; the graph would be an arc.
The relationship is non-proportional; the graph would be an arc.

The proportional relationship cannot be determined from the information provided.
The proportional relationship cannot be determined from the information provided.
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Answer 3

To determine if the relationship between time walking and calories burned is proportional, we need to check if the ratios of calories burned to time walked are constant.

We can calculate the calories burned per minute for each entry:

• For 20 minutes: \( \frac{100 \text{ calories}}{20 \text{ minutes}} = 5 \text{ calories/minute} \)
• For 30 minutes: \( \frac{150 \text{ calories}}{30 \text{ minutes}} = 5 \text{ calories/minute} \)
• For 40 minutes: \( \frac{200 \text{ calories}}{40 \text{ minutes}} = 5 \text{ calories/minute} \)
• For 60 minutes: \( \frac{300 \text{ calories}}{60 \text{ minutes}} = 5 \text{ calories/minute} \)
• For 80 minutes: \( \frac{400 \text{ calories}}{80 \text{ minutes}} = 5 \text{ calories/minute} \)

Since the ratio of calories burned per minute is constant at 5 calories per minute, the relationship is proportional. Therefore, the correct response is:

The relationship is proportional.