Question

1. carson practices each day to prepare for an upcoming race. he starts the day by running 2 miles and then walking at a rate of 4 miles per hour. which representations show the relationship between the total number of miles he covers in a day, y, and the number of hours he walks, x? a. carsons practice number of hours walked, x total number of miles, y 1 6 1.5 8 2 10 2.5 12 b. carsons practice number of hours walked, x total number of miles, y 1 6 1.5 7 2 8 2.5 9 c. y = 2x + 4 d. y = 4x + 2 e. graph of total miles vs hours walked with y-intercept 2 f. graph of total miles vs hours walked with y-intercept 4

Explanation:

Step1: Determine the equation

Carson runs 2 miles first, then walks at 4 miles per hour. So the total miles \( y \) is the initial 2 miles plus the miles walked (which is \( 4x \), since distance = rate × time). So the equation is \( y = 4x + 2 \).

Step2: Check Option A

For \( x = 1 \), \( y = 4(1)+2 = 6 \). For \( x = 1.5 \), \( y = 4(1.5)+2 = 8 \). For \( x = 2 \), \( y = 4(2)+2 = 10 \). For \( x = 2.5 \), \( y = 4(2.5)+2 = 12 \). This matches the table in A.

Step3: Check Option B

For \( x = 1 \), \( y = 4(1)+2 = 6 \), but B has \( y = 6 \) for \( x = 1 \), \( y = 7 \) for \( x = 1.5 \) (should be 8), so B is wrong.

Step4: Check Option C

Equation is \( y = 2x + 4 \), which doesn't match our derived equation \( y = 4x + 2 \), so C is wrong.

Step5: Check Option D

Equation is \( y = 4x + 2 \), which matches our derived equation, so D is correct.

Step6: Check Option E

Graph E: The y - intercept should be 2 (from \( y = 4x + 2 \)). If we check the slope, the equation here is \( y = 2x + 4 \), which has a slope of 2, not 4. So E is wrong.

Step7: Check Option F

Graph F: The y - intercept here looks like 4 (from the graph), but our equation has a y - intercept of 2. So F is wrong.

Answer:

A, D