For Uber, express in a table the cost of the ride given the number of miles provided.
Number of miles: 5, 10, 20
Total Cost (dollars): 13.30, 22.96, 29.92
Write an equation in slope-intercept, point-slope, or standard form. Explain why you chose the form you did.
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What does the slope mean in the context of the problem?
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Based on the given information, the table can be represented in slope-intercept form as:
Total Cost = (Rate per mile) * (Number of miles) + (Fixed cost)
To find the rate per mile, we can calculate the difference in total cost for every one mile increase in distance. Choosing slope-intercept form allows us to directly determine both the rate per mile and the fixed cost.
In this case, the rate per mile can be calculated using the given information as:
Rate per mile = (Total Cost for 10 miles - Total Cost for 5 miles) / (10 - 5)
= (22.96 - 13.30) / 5
= 9.66 / 5
= 1.93
We can also determine the fixed cost by observing the table. When the number of miles is 0, the cost is $0. Therefore, the fixed cost is $0.
The equation in slope-intercept form is:
Total Cost = 1.93 * Number of miles + 0
The slope of the equation (1.93 in this case) represents the rate per mile. In the context of the problem, it indicates how much the cost increases for each additional mile traveled.
can you explain why you are using the slope-intercept form?
Certainly! I chose to use the slope-intercept form because it directly represents the relationship between the two variables in the problem: the total cost of the ride and the number of miles traveled.
The slope-intercept form is written as "y = mx + b," where "y" represents the dependent variable (total cost), "x" represents the independent variable (number of miles), "m" represents the slope (rate per mile), and "b" represents the y-intercept (fixed cost).
In this problem, we are given data points for the number of miles and the corresponding total cost. By finding the difference in total cost for every one mile increase in distance, we can calculate the slope, which represents the rate per mile. Additionally, observing that the cost is $0 when the number of miles is 0 allows us to determine the y-intercept, which is $0.
Using the slope-intercept form allows us to easily express the relationship between the variables, calculate the rate per mile, and find the fixed cost. It also provides a clear and understandable equation that can be used to calculate the total cost for any given number of miles.
To create a table for the cost of the Uber ride based on the number of miles, you need to observe the given data and identify a pattern or relationship between the variables.
From the information provided, we can see that as the number of miles increases, the total cost of the ride also increases. This suggests a linear relationship between the two variables.
To find the equation representing this relationship, we can use either the slope-intercept form (y = mx + b), point-slope form (y - y1 = m(x - x1)), or standard form (Ax + By = C) depending on the given information and personal preference.
Let's use the slope-intercept form, y = mx + b, where y represents the total cost of the ride, x represents the number of miles, m represents the slope, and b represents the y-intercept.
We need to find the slope (m) and the y-intercept (b) using the given data points:
Number of miles: 5, 10, 20
Total Cost (dollars): 13.30, 22.96, 29.92
To find the slope, we can choose any two points from the data and use the formula: m = (y2 - y1) / (x2 - x1).
Let's take the points (5, 13.30) and (10, 22.96):
m = (22.96 - 13.30) / (10 - 5) = 9.66 / 5 = 1.932
Now, we can substitute one of the data points (x, y) and the slope (m) into the slope-intercept form and solve for the y-intercept (b).
Using the point (5, 13.30):
13.30 = 1.932(5) + b
13.30 = 9.66 + b
b = 3.64
Therefore, the equation in slope-intercept form is:
y = 1.932x + 3.64
In this context, the slope (1.932) represents the rate of change in the total cost of the Uber ride per unit of distance (in this case, dollars per mile). It indicates that for each additional mile, the cost of the ride increases by approximately $1.932.
The y-intercept (3.64) represents the starting cost of the Uber ride, regardless of the distance traveled. In this case, it suggests that even if you travel zero miles, there will still be a base cost of $3.64 for the ride.