Answer :
To solve for the slope of the function given the points in the table, we must use the formula for the slope of a line between two points, which is given by:
[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are two points on the line. Let's choose the points furthest apart from the table to ensure we capture the overall rate of change accurately:
Using the points [tex]\((2, 8.50)\)[/tex] and [tex]\((12, 31.00)\)[/tex]:
1. Calculate the change in miles ([tex]\(\Delta x\)[/tex]):
[tex]\[ \Delta x = x_2 - x_1 = 12 - 2 = 10 \][/tex]
2. Calculate the change in cost ([tex]\(\Delta y\)[/tex]):
[tex]\[ \Delta y = y_2 - y_1 = 31.00 - 8.50 = 22.50 \][/tex]
3. Now, substitute [tex]\(\Delta x\)[/tex] and [tex]\(\Delta y\)[/tex] into the slope formula:
[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{22.50}{10} = 2.25 \][/tex]
So, the slope of the function is:
[tex]\[ 2.25 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{2.25} \][/tex]
[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are two points on the line. Let's choose the points furthest apart from the table to ensure we capture the overall rate of change accurately:
Using the points [tex]\((2, 8.50)\)[/tex] and [tex]\((12, 31.00)\)[/tex]:
1. Calculate the change in miles ([tex]\(\Delta x\)[/tex]):
[tex]\[ \Delta x = x_2 - x_1 = 12 - 2 = 10 \][/tex]
2. Calculate the change in cost ([tex]\(\Delta y\)[/tex]):
[tex]\[ \Delta y = y_2 - y_1 = 31.00 - 8.50 = 22.50 \][/tex]
3. Now, substitute [tex]\(\Delta x\)[/tex] and [tex]\(\Delta y\)[/tex] into the slope formula:
[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{22.50}{10} = 2.25 \][/tex]
So, the slope of the function is:
[tex]\[ 2.25 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{2.25} \][/tex]
