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. carson’s practice number of hours walked, x total number of miles, y 1 6 1.5 8 2 10 2.5 12 b. carson’s 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. total number of miles (graph with x-axis number hours walked, y-axis total number of miles, starting at (0,2)) f. total number of miles (graph with x-axis number hours walked, y-axis total number of miles, starting at (0,4))

Explanation:

Step1: Determine the equation

Carson runs 2 miles first, then walks at 4 miles per hour. So the total miles \( y = 4x + 2 \), where \( x \) is hours walked.

Step2: Check Option A

For \( x = 1 \), \( y = 4(1)+2 = 6 \) (matches). \( x = 1.5 \), \( y = 4(1.5)+2 = 8 \) (matches). \( x = 2 \), \( y = 4(2)+2 = 10 \) (matches). \( x = 2.5 \), \( y = 4(2.5)+2 = 12 \) (matches). So A is correct.

Step3: Check Option B

For \( x = 1 \), \( y = 6 \) (matches \( 4(1)+2 = 6 \)). \( x = 1.5 \), \( y = 7 \), but \( 4(1.5)+2 = 8
eq 7 \). So B is wrong.

Step4: Check Option C

Equation \( y = 2x + 4 \) doesn't match \( y = 4x + 2 \). So C is wrong.

Step5: Check Option D

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

Step6: Check Option E

The graph starts at \( y = 2 \) (when \( x = 0 \), \( y = 2 \)) and has slope 4 (since \( y = 4x + 2 \), slope is 4). Let's check \( x = 1 \), \( y = 6 \) (matches). The graph's slope and y - intercept match. So E is correct.

Step7: Check Option F

The graph starts at \( y = 4 \) (when \( x = 0 \)), but our equation has \( y = 2 \) when \( x = 0 \). So F is wrong.

Answer:

A. Carson’s Practice table (with x=1,y=6; x=1.5,y=8; x=2,y=10; x=2.5,y=12), D. \( y = 4x + 2 \), E. The graph with y - intercept 2 and slope 4 (labeled E)