a 2-mi cab ride costs $4.25. a 7-mi cab ride costs $8.50. which equation models the cost y of a cab ride that is x miles?
a+2b = 4.25
a+7b = 8.50
(a,b) = (51/20,17/20)
so,
y = 2.55 + .85x
The time t required to drive a certain distance varies inversely with the speed r. If it takes 2 hours to drive the distance at 30 miles per hour, how long will it take to drive the same distance at 50 miles per hour?
Why did the math book go to the party?
Because it wanted to find the 'x' for a good time!
Now, back to the question at hand. Let's find the equation that models the cost y of a cab ride that is x miles based on the given information.
We can start by noticing that the cost increases as the distance traveled increases. So, we know there is a linear relationship between the distance and the cost.
Let's use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Now, let's find the slope. We can calculate it by taking the change in y over the change in x. So, for the given information:
Slope = (8.50 - 4.25) / (7 - 2) = 4.25 / 5 = 0.85
Now, we can plug the slope and any point (x, y) from the given information into the equation.
Using the point (2, 4.25):
4.25 = 0.85 * 2 + b
4.25 = 1.70 + b
b = 4.25 - 1.70
b = 2.55
So, the equation that models the cost y of a cab ride that is x miles is:
y = 0.85x + 2.55
To find the equation that models the cost y of a cab ride that is x miles, we need to determine the rate of cost per mile.
We are given two data points:
- A 2-mile cab ride costs $4.25.
- A 7-mile cab ride costs $8.50.
To find the rate of cost per mile, we can calculate the difference in cost for the two distances and divide it by the difference in miles:
Rate = (Cost of 7-mile ride - Cost of 2-mile ride) / (7 miles - 2 miles)
Rate = ($8.50 - $4.25) / (7 - 2)
Rate = $4.25 / 5
Rate = $0.85
Now we have the rate of $0.85 per mile.
To model the cost y of a cab ride that is x miles, we can use the equation: y = mx + b, where m is the slope (rate of cost per mile) and b is the y-intercept (initial cost).
Substituting the values we have:
y = 0.85x + b
To find the value of b, we can substitute one of the data points' values for x and y. Let's use the 2-mile ride, where the cost is $4.25:
4.25 = 0.85(2) + b
4.25 = 1.7 + b
b = 4.25 - 1.7
b = 2.55
The equation that models the cost y of a cab ride that is x miles is:
y = 0.85x + 2.55