A 5-mile cab ride costs $9.30. A 11-mile cab ride costs $17.70. Find a linear equation that models cost c as a function of distance d.
Treat the data as two ordered pairs (5,930) and (11,1770) of the form (d,c)
take the slope, then find the equation in the form
c = md + b ( just like y = mx + b)
To find a linear equation that models the cost c as a function of the distance d, we can use the two points given: (5, 9.30) and (11, 17.70).
The equation of a linear function is given by y = mx + b, where m is the slope and b is the y-intercept. In this case, c represents the cost, which is the y-value, and d represents the distance, which is the x-value.
First, let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the two points (5, 9.30) and (11, 17.70):
m = (17.70 - 9.30) / (11 - 5)
m = 8.40 / 6
m = 1.40
Now that we have the slope, let's substitute one of the points into the equation y = mx + b to solve for b (the y-intercept).
Using the point (5, 9.30):
9.30 = 1.40 * 5 + b
9.30 = 7 + b
b = 9.30 - 7
b = 2.30
Now, we have the values of m and b, so we can write the linear equation:
c = 1.40d + 2.30
Therefore, the linear equation that models the cost c as a function of the distance d is c = 1.40d + 2.30.