A 3-mi cab ride costs $3.00. A 6-mi cab ride costs $4.80. Find a linear equation that models cost c as a function of distance d. write your linear equation using function notation.
c = f(d) = m d + b
3 = m (3) + b
4.8 = m (6) + b
subtract
-1.8 = -3m
m = 1.8/3 = .6
find b
3 = .6 (3) +b
b = .4(3) = 1.2
so
c = .6 d + 1.2
To find the linear equation that models the cost as a function of distance, we can use the given information to determine the slope and the y-intercept of the equation.
Let's start by determining the slope (m) of the equation. The slope represents the rate of change of the cost with respect to distance. We can find the slope by dividing the change in cost by the change in distance:
Slope (m) = (Change in cost) / (Change in distance)
For the given information:
Change in cost = $4.80 - $3.00 = $1.80
Change in distance = 6 mi - 3 mi = 3 mi
Slope (m) = $1.80 / 3 mi = $0.60/mi
Now, we need to find the y-intercept (b) of the equation. The y-intercept represents the starting cost when the distance is 0.
From the given information, we know that a 3-mi cab ride costs $3.00. Therefore, when the distance (d) is 0, the cost (c) will also be $3.00.
y-intercept (b) = $3.00
Now, we can write the linear equation using the slope-intercept form:
c = md + b
Plugging in the values we found:
c = ($0.60/mi)d + $3.00
In function notation, the linear equation that models the cost as a function of distance is:
c(d) = 0.60d + 3.00