To take a taxi in downtown, it will cost you $3.00 to go a mile. After 6 miles, it will cost $5.25. The cost varies linearly with the distance traveled. Write the equation expressing cost (c) in terms of miles (d) traveled.
c is cost and d is miles traveled? K.
c = 3 + .45d.
Based on the wording, it appears it cost 3 dollars for the first mile and .45 for the next 5 bringing the total to 5.25 for 6 miles.
So $3 is the base, or the constant, and each additional mile is 45 cents.
How is this the solution if 3 + .45d does NOT equal the cost of $5.25 when the taxi is used for the 6 miles? Check your solution please. The proper solution is given by the following equation: C(d) = .45d + 2.55 and is found by taking the $3 constant cost for the 1 mile + .45 slope TIMES (miles driven OVER the 1 mile...expressed as (d - 1) After simplifying...you get solution...so...
C(d)= 3 + ,45(d-1) which is 3+.45d-.45
which then becomes... .45d + 2.55
To write the equation representing the relationship between cost (c) and miles traveled (d), we need to determine the slope and the y-intercept of the linear equation.
First, let's calculate the slope:
We know that it costs $3.00 to go 1 mile. So, the cost of traveling one mile is $3.00.
Next, we can use the formula for slope: slope = (change in cost) / (change in distance).
Here, the change in cost is $5.25 - $3.00 = $2.25 (since the total cost after 6 miles is $5.25 and the initial cost for 1 mile is $3.00).
The change in distance is 6 miles - 1 mile = 5 miles (since we are finding the difference between the distances traveled).
Therefore, the slope (m) of the linear equation is:
m = (change in cost) / (change in distance) = $2.25 / 5 miles = $0.45 per mile.
Now, let's find the y-intercept:
The initial cost for 1 mile is $3.00. So, at d = 0 (representing no distance traveled), the cost (c) would also be $3.00.
Therefore, the y-intercept (b) is $3.00.
Now that we have the slope (m = 0.45) and the y-intercept (b = 3.00), we can write the equation for the cost (c) in terms of miles (d) traveled:
c = m * d + b
c = 0.45d + 3.00
Hence, the equation expressing the cost (c) in terms of miles (d) traveled is c = 0.45d + 3.00.