The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $310 for 140 mi and in June her cost was $450 for 700 mi. Assume that there is a linear relationship between the monthly cost C of driving a car and the distance driven d.
ok. sounds good to me.
To find the linear relationship between the monthly cost C of driving a car and the distance driven d, we need to determine the equation of a straight line that represents this relationship.
We are given two data points:
- In May, the driving cost was $310 for 140 miles.
- In June, the driving cost was $450 for 700 miles.
Let's assign May as Point 1, with coordinates (140, 310), and June as Point 2, with coordinates (700, 450).
First, we need to find the slope of the line, which represents the rate of change of the monthly cost with respect to the distance driven. The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates:
m = (450 - 310) / (700 - 140)
= 140 / 560
= 0.25
Now that we have the slope, we can find the equation of the line using the point-slope form:
y - y1 = m(x - x1)
Using Point 1 (140, 310):
y - 310 = 0.25(x - 140)
Expanding:
y - 310 = 0.25x - 35
Rearranging the equation to slope-intercept form (y = mx + b):
y = 0.25x - 35 + 310
= 0.25x + 275
Therefore, the linear relationship between the monthly cost C of driving a car and the distance driven d is:
C = 0.25d + 275
This equation represents how the monthly cost of driving a car changes with the number of miles driven.