A 2 mile cab cost $5. A 6 mile cab costs $9. Write an equation to model the cost: c of a cab ride miles: m.
You have two points on the line: (2,5) and (6,9).
So, the line has slope=1, and its equation is
c = m-3
To write an equation that models the cost of the cab ride based on the number of miles, we need to determine the relationship between the cost and the distance traveled. Let's analyze the given information:
- A 2-mile cab ride costs $5.
- A 6-mile cab ride costs $9.
We can see that as the distance increases, the cost of the cab ride also increases. This implies that there is a linear relationship between the distance and the cost.
To find the equation that models this relationship, we need to determine the slope and the y-intercept of the line.
Let's define the variables:
- c: the cost of the cab ride (in dollars).
- m: the distance traveled (in miles).
Now, let's find the slope:
The slope, often represented by the letter 'm', represents the amount the cost changes for each unit of distance. To obtain the slope, we can use the following formula:
slope = (change in cost) / (change in distance)
For the given information, when the distance changes from 2 miles to 6 miles, the cost changes from $5 to $9. Therefore, the change in cost is $9 - $5 = $4, and the change in distance is 6 - 2 = 4 miles.
slope = (change in cost) / (change in distance) = $4 / 4 miles = $1 per mile.
Now that we have the slope, let's find the y-intercept:
The y-intercept, often represented by the letter 'b', is the value of the cost when the distance is zero. Looking at the given information, we do not have a specific cost listed for a zero-mile ride. Therefore, we need to assume an initial cost.
Based on the information given, let's assume that the initial cost is $3 for a zero-mile ride. You can choose a different assumption if desired.
The equation that models the cost 'c' of a cab ride based on the miles 'm' can be written in slope-intercept form as:
c = m × slope + b
Plugging in our values, we have:
c = m × $1 + $3
Simplifying the equation, we get:
c = $1m + $3
Therefore, the equation that models the cost 'c' of a cab ride (in dollars) based on the miles 'm' is:
c = $1m + $3