Question

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? select three correct answers. carsons practice number of hours walked, x total number of miles, y 1 6 1.5 8 2 10 2.5 12 carsons practice number of hours walked, x total number of miles, y 1 6 1.5 7 2 8 2.5 9 y = 2x + 4 y = 4x + 2 carsons practice carsons practice total number of miles total number of miles 1 2 3 x 1 2 3 x number of number of hours walked hours walked

Explanation:

Step1: Determine the linear - equation formula

Carson starts by running 2 miles and walks at a rate of 4 miles per hour. The total number of miles \(y\) he covers in a day is given by the linear - equation \(y = 4x+2\), where \(x\) is the number of hours he walks.

Step2: Check the table values

For the first table:
When \(x = 1\), \(y=4\times1 + 2=6\); when \(x = 1.5\), \(y=4\times1.5+2=6 + 2=8\); when \(x = 2\), \(y=4\times2+2=8 + 2=10\); when \(x = 2.5\), \(y=4\times2.5+2=10 + 2=12\). This table satisfies the equation \(y = 4x + 2\).
For the second table:
When \(x = 1\), \(y=4\times1+2 = 6
eq7\). This table does not satisfy the equation \(y = 4x + 2\).

Step3: Check the graphs

The graph of the equation \(y=4x + 2\) has a \(y\) - intercept of 2 (the value of \(y\) when \(x = 0\)) and a slope of 4. The first graph with a \(y\) - intercept of 2 and a positive slope of 4 is correct. The second graph with a different \(y\) - intercept or slope is incorrect.

Answer:

1. The first table (with values \(x = 1,y = 6\); \(x = 1.5,y = 8\); \(x = 2,y = 10\); \(x = 2.5,y = 12\))
2. The equation \(y = 4x+2\)
3. The first graph (with \(y\) - intercept at 2 and positive slope)