To find the equation of the linear function that models the relationship shown in the table, we can use the coordinates provided:
- (4, 38)
- (6, 58)
First, we calculate the slope (m) of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (4, 38) and (6, 58):
- \(x_1 = 4, y_1 = 38\)
- \(x_2 = 6, y_2 = 58\)
Now plug in the values: \[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]
Now we have the slope \(m = 10\).
Next, we can use the point-slope form of the equation, which is: \[ y - y_1 = m(x - x_1) \]
Using the point (4, 38): \[ y - 38 = 10(x - 4) \]
Distributing the 10: \[ y - 38 = 10x - 40 \]
Adding 38 to both sides: \[ y = 10x - 2 \]
Thus, the equation of the linear function that models the relationship shown in the table is:
y = 10x - 2
So the correct response is: y = 10x − 2