the graph shows the amount of money miguel earns after working x hours.\namount earned vs. hours…

the graph shows the amount of money miguel earns after working x hours.\namount earned vs. hours worked\nwhat is the rate of change of the amount earned with respect to hours worked for this function?\n○ \\(\\frac{1}{13}\\) hours per dollar\n○ \\(\\frac{2}{5}\\) hours per dollar\n○ 3 dollars per hour\n○ 13 dollars per hour

the graph shows the amount of money miguel earns after working x hours.\namount earned vs. hours worked\nwhat is the rate of change of the amount earned with respect to hours worked for this function?\n○ \\(\\frac{1}{13}\\) hours per dollar\n○ \\(\\frac{2}{5}\\) hours per dollar\n○ 3 dollars per hour\n○ 13 dollars per hour

Answer

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) for a linear function is given by ( m=\frac{y_2 - y_1}{x_2 - x_1} ), where ((x_1,y_1)) and ((x_2,y_2)) are two points on the line. We have two points: ((2,26)) and ((5,65)).

Step2: Substitute values into formula

Substitute ( x_1 = 2, y_1 = 26, x_2 = 5, y_2 = 65 ) into the slope formula: ( m=\frac{65 - 26}{5 - 2}=\frac{39}{3}=13 ). This means the rate of change is 13 dollars per hour (since y is amount earned and x is hours worked, slope is dollars per hour).

Answer:

13 dollars per hour