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Question 1
(6 points)
Part A. Consider the points (3, 30) and (12, 120).

The rise from (3, 30) to (12,120) =
. Enter your answer as a whole number.

The run from (3, 30) to (12, 120) =
. Enter your answer as a whole number.

The slope of the line from (3, 30) to (12, 120) = riserun
=
. Remember to simplify the slope.

Part B. Consider the points (0, 0) and (6, 60).

The rise from (0, 0) to (6, 60) =
. Enter your answer as a whole number.

The run from (0, 0) to (6, 60) =
. Enter your answer as a whole number.

The slope of the line from (0, 0) to (6, 60) = riserun
=
. Remember to simplify the slope.

Question 2
Part C. Compare the slopes from Part A and Part B.(1 point)
The slope from (0,0) to (6, 60) is
to the slope from (3, 30) to (12, 120).

1 answer

Let's solve the questions step by step.

Question 1

Part A: Evaluate the points (3, 30) and (12, 120)

  1. Calculate the rise:

    • Rise = \( y_2 - y_1 = 120 - 30 = 90 \)

  2. Calculate the run:

    • Run = \( x_2 - x_1 = 12 - 3 = 9 \)

  3. Calculate the slope:

    • Slope = Rise / Run = \( \frac{90}{9} = 10 \)

To summarize:

  • The rise from (3, 30) to (12, 120) = 90
  • The run from (3, 30) to (12, 120) = 9
  • The slope of the line from (3, 30) to (12, 120) = 10

Part B: Evaluate the points (0, 0) and (6, 60)

  1. Calculate the rise:

    • Rise = \( y_2 - y_1 = 60 - 0 = 60 \)

  2. Calculate the run:

    • Run = \( x_2 - x_1 = 6 - 0 = 6 \)

  3. Calculate the slope:

    • Slope = Rise / Run = \( \frac{60}{6} = 10 \)

To summarize:

  • The rise from (0, 0) to (6, 60) = 60
  • The run from (0, 0) to (6, 60) = 6
  • The slope of the line from (0, 0) to (6, 60) = 10

Question 2

Part C: Compare the slopes from Part A and Part B.

  • The slope from (0, 0) to (6, 60) is equal to the slope from (3, 30) to (12, 120).

So for the comparison:

  • The slope from (0, 0) to (6, 60) is equal to the slope from (3, 30) to (12, 120).