Question

1. shawn wants to increase the number of laps he can run on a track. he decides 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. which statement about shawns line is true? a. the slope of the line is 1/3 b. the y - intercept of the line is (4,0). c. the y - intercept means that shawn ran 4 laps at week 0. d. the slope represents the average number of weeks it takes shawn to run a lap.

Explanation:

Step1: Recall the slope - intercept form of a line

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. The \(y\) - intercept is the value of \(y\) when \(x = 0\).

Step2: Analyze each option

• Option A:

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's assume two points \((x_1,y_1)=(0,4)\) and \((x_2,y_2)=(12,0)\). Then \(m=\frac{0 - 4}{12-0}=-\frac{1}{3}
eq\frac{1}{3}\).

• Option B:

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

• Option C:

The \(y\) - intercept is the value of \(y\) when \(x = 0\). When \(x = 0\) (week \(0\)), \(y = 4\) (number of laps). So the \(y\) - intercept means that Shawn ran \(4\) laps at week \(0\).

• Option D:

The slope \(m =-\frac{1}{3}\). The slope represents the change in the number of laps per week (not the average number of weeks per lap). The negative slope means the number of laps is decreasing per week.

Answer:

C. The \(y\) - intercept means that Shawn ran \(4\) laps at week \(0\).