For the second company, express in a table the cost of the cab ride given the number of miles provided.
Number of Miles 0 1 2 3 4 5
Total Cost (dollars)
a. For the second company write an equation in point-slope form.
b. What does the slope mean in the context of the problem?
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Helpful forms
Slope-Intercept Form y=mx+b
Point-Slope Form y-y_1=m(x-x_1)
a. Sure, here's a table expressing the cost of the cab ride for the second company given the number of miles provided:
Number of Miles | Total Cost (dollars)
-------------------------------------
0 |
1 |
2 |
3 |
4 |
5 |
b. Now, for the equation in point-slope form, we need a point that lies on the line. Let's assume that when the number of miles is 0, the total cost is $10. This gives us the point (0, 10).
So, using the point-slope form (y - y₁) = m(x - x₁), we can substitute the values:
(y - 10) = m(x - 0)
Now, we need to find the value of the slope (m). For that, we can find two other points on the line. Let's say when the number of miles is 1, the total cost is $12, and when the number of miles is 2, the total cost is $14.
With these points (1, 12) and (2, 14), we can find the slope using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
m = (14 - 12) / (2 - 1)
m = 2 / 1
m = 2
Now we have the slope (m = 2) and the point (0, 10), we can go back to the point-slope form and replace the corresponding values:
(y - 10) = 2(x - 0)
Simplifying the equation, we get:
y - 10 = 2x
And that's the equation in point-slope form for the second company's cab ride cost.
b. In the context of the problem, the slope (m = 2) represents the rate at which the cost of the cab ride increases with each additional mile. For every mile traveled, the cost increases by $2. So, for example, if you travel 3 miles, the total cost would be $10 + (3 * $2) = $16.
To express the cost of the cab ride given the number of miles provided in a table, we need more information about the pricing structure of the second company. Without that information, we cannot fill in the table.
However, I can still help you with parts "a" and "b" of the question.
a. To write an equation in point-slope form for the second company, we need two pieces of information: one point on the line and the slope of the line. Without this information, we cannot determine the equation in point-slope form.
b. The slope of a line in the context of this problem represents the cost per mile. It shows how much the cab fare increases or decreases for each additional mile.
To express the cost of the cab ride in a table given the number of miles provided, we can use the point-slope form and an equation to find the total cost.
a. Firstly, we need to determine the cost for each mile. Let's assume that the cost per mile is a constant value.
Let's say the cost per mile for the second company is $2. We can now calculate the total cost for each number of miles:
Number of Miles | Total Cost (dollars)
---------------------------------------
0 | $0
1 | $2
2 | $4
3 | $6
4 | $8
5 | $10
The total cost increases by $2 for each additional mile.
To express this relationship in point-slope form, we can choose any point on the line and use the formula:
y - y1 = m(x - x1)
Let's select the point (0, 0) since it lies on the line. So, x1 = 0 and y1 = 0. The slope, m, represents the rate at which the total cost increases per mile, which in this case is $2.
Using the values, we have:
y - 0 = 2(x - 0)
This equation simplifies to:
y = 2x
So, the equation in point-slope form for the second company is y = 2x.
b. In the context of the problem, the slope (2 in this case) represents the cost per mile for the cab ride. It indicates that for every mile traveled, the cost increases by $2.
Curious about the first company.
Also curious where to find the data for the cost per mile.