Question

shawn wants to increase the number of laps he can run on a track. he plans to add the same number of laps to his run each week.
he makes a graph to show the number of laps he is scheduled to run each week.

(7) which statement about shawn’s line is true?
a) the slope of the line is (\frac{1}{4}).
b) the (y)-intercept of the line is ((4, 0)).
c) the (y)-intercept means shawn ran 4 laps at week 0.
d) the slope represents the average number of weeks it takes shawn to run a lap.

Explanation:

To solve this, we analyze the graph and each statement:

Step 1: Analyze the graph's axes

The \( x \)-axis is "Week" (from 0 to 10), and the \( y \)-axis is "Number of Laps" (from 0 to 20). The line starts at \( (0, 4) \) (when Week = 0, Laps = 4) and goes up, so it’s a linear relationship.

Step 2: Evaluate each statement

• Statement 1: "The slope of the line is \( \frac{1}{4} \)."

Slope formula: \( m = \frac{\Delta y}{\Delta x} \). Take two points: \( (0, 4) \) and, say, \( (4, 8) \) (from the graph’s grid). \( \Delta y = 8 - 4 = 4 \), \( \Delta x = 4 - 0 = 4 \). So \( m = \frac{4}{4} = 1 \), not \( \frac{1}{4} \). Incorrect.

• Statement 2: "The \( y \)-intercept of the line is \( (4, 0) \)."

The \( y \)-intercept is where \( x = 0 \). From the graph, when \( x = 0 \), \( y = 4 \), so the \( y \)-intercept is \( (0, 4) \), not \( (4, 0) \). Incorrect.

• Statement 3: "The \( y \)-intercept means Shawn ran 4 laps at week 0."

The \( y \)-intercept is \( (0, 4) \), so when Week (\( x \)) = 0, Laps (\( y \)) = 4. This matches: at week 0, he ran 4 laps. Correct.

• Statement 4: "The slope represents the average number of weeks it takes Shawn to run a lap."

Slope is \( \frac{\text{change in laps}}{\text{change in weeks}} \), so it represents laps per week (not weeks per lap). Incorrect.

Answer:

The correct statement is: "The \( y \)-intercept means Shawn ran 4 laps at week 0." (The option with this text, e.g., the third radio button’s statement.)