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Math  /  Algebra

QuestionShort Response
6. Robi has run the first 4 miles of a race in 30 minutes. She reached the 6 mile point after 45 minutes. Without graphing, is the slope of the line that represents this situation positive, negative, zero, or undefined? Wh is the slope?
Prentice Hall Algebra 1 - Të̉aching Resources Copyright ⊙\odot by Pearson Education, Inc., or its affiliates. All Rights Reserved. 7

Studdy Solution

STEP 1

1. The slope of a line is calculated as the change in the vertical axis divided by the change in the horizontal axis.
2. The situation describes Robi's running distance over time.
3. The points given are (4, 30) and (6, 45), where the first coordinate is miles and the second is minutes.

STEP 2

1. Identify the coordinates representing the situation.
2. Calculate the slope using the formula for slope.
3. Determine the nature of the slope (positive, negative, zero, or undefined).

STEP 3

Identify the coordinates from the problem. The first point is (4, 30) and the second point is (6, 45).

STEP 4

Use the slope formula m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1} where (x1,y1)=(4,30) (x_1, y_1) = (4, 30) and (x2,y2)=(6,45) (x_2, y_2) = (6, 45) .
Calculate the difference in the y-values: y2−y1=45−30=15 y_2 - y_1 = 45 - 30 = 15 .
Calculate the difference in the x-values: x2−x1=6−4=2 x_2 - x_1 = 6 - 4 = 2 .

STEP 5

Substitute the differences into the slope formula:
m=152=7.5 m = \frac{15}{2} = 7.5

STEP 6

Since the slope m=7.5 m = 7.5 is a positive number, the slope of the line is positive.
The slope of the line is positive and its value is:
7.5 \boxed{7.5}

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