A five mile cab ride costs $7.20. A nine mile cab ride costs $11.60. Find the linear equation that models a relationship between cost c and distance d
c=1.44d+4.40
d=1.10c+4.40
c=1.29d+1.70
c=1.10d+1.70
c = 1.44d + 4.40
To find the linear equation that models the relationship between cost c and distance d, we need to use the information given.
We are given two data points:
- A five-mile cab ride costs $7.20 (c=7.20, d=5)
- A nine-mile cab ride costs $11.60 (c=11.60, d=9)
To find the equation, we can use the slope-intercept form: y = mx + b, where y is the cost (c), x is the distance (d), m is the slope, and b is the y-intercept.
First, let's find the slope (m):
m = (y2 - y1) / (x2 - x1)
= (11.60 - 7.20) / (9 - 5)
= 4.40 / 4
= 1.10
Now, let's find the y-intercept (b) by substituting one of the data points into the equation:
7.20 = 1.10 * 5 + b
7.20 = 5.50 + b
b = 7.20 - 5.50
b = 1.70
Therefore, the linear equation that models the relationship between cost c and distance d is:
c = 1.10d + 1.70
So, option d: c = 1.10d + 1.70 is the correct equation.
To find the linear equation that models the relationship between cost c and distance d, we need to consider the given information.
We have two data points:
- A five-mile cab ride costs $7.20
- A nine-mile cab ride costs $11.60
Let's assign the variables d and c to distance and cost respectively. We can set up two equations using these data points:
For the five-mile cab ride:
c = 7.20
d = 5
For the nine-mile cab ride:
c = 11.60
d = 9
We need to find the equation in the form c = md + b, where m is the slope (rate of change) and b is the y-intercept.
To find the slope (m), we can use the formula:
m = (c2 - c1) / (d2 - d1)
Using the two data points:
m = (11.60 - 7.20) / (9 - 5)
m = 4.40 / 4
m = 1.10
Now, we can substitute the slope (m) into the equation and solve for the y-intercept (b). We can use either of the data points:
Using the five-mile cab ride data (d = 5, c = 7.20):
c = md + b
7.20 = 1.10 * 5 + b
7.20 = 5.50 + b
b = 7.20 - 5.50
b = 1.70
Therefore, the linear equation that models the relationship between cost c and distance d is:
c = 1.10d + 1.70
So, the correct linear equation is c = 1.10d + 1.70.