A 3-mile cab ride cost $3.00. A 6-mile cab ride cost $4.80. Find a linear equation that models cost c as a function of distance d
slope of linear equation is
(4.8 - 3)/(6 - 3) = 1.8/3 = 0.6
c - 3 = 0.6(d - 3)
c - 3 = 0.6d - 1.8
c = 0.6d + 1.2
To find a linear equation that models the cost c as a function of distance d, we can use the given information from the two cab rides.
Let's analyze the first cab ride:
Distance: 3 miles
Cost: $3.00
We can represent this information as a coordinate point (3, 3.00).
Now, let's analyze the second cab ride:
Distance: 6 miles
Cost: $4.80
This can be represented as another coordinate point (6, 4.80).
Now, we can use the two points (3, 3.00) and (6, 4.80) to find the linear equation.
The equation of a straight line can be represented as y = mx + b, where:
- y is the dependent variable (cost in this case)
- x is the independent variable (distance in this case)
- m is the slope of the line
- b is the y-intercept of the line
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (3, 3.00) and (6, 4.80):
m = (4.80 - 3.00) / (6 - 3)
m = 1.80 / 3
m = 0.60
Now that we have the slope (m), we can find the y-intercept (b) by substituting one of the points into the equation y = mx + b. Let's use the point (3, 3.00):
3.00 = (0.60)(3) + b
3.00 = 1.80 + b
b = 3.00 - 1.80
b = 1.20
Now that we have the slope (m = 0.60) and the y-intercept (b = 1.20), we can write the linear equation that models the cost c as a function of distance d:
c = 0.60d + 1.20
Therefore, the linear equation that models the cost c as a function of distance d is c = 0.60d + 1.20.