a)Write an equation for the line that passes through the points (0,5) and (4,12). Use any valid form of a linear line.

b)You are taking a Yellow Cab in St. Paul from Como Park to the State Capitol (a 3.2 mile trek). When you get in, you are charged $6.90 for the likely amount of time spent in the cab. They also charge $2.50 per mile. What will be your fare at the end, without tips? YOU MUST WRITE A LINEAR EQUATION THAT RELATES THE FARE TO THE DISTANCE TRAVELED, AND SOLVE THAT EQUATION.

clearly (0,5) is the y-intercept, so all we need is the slope

slope = (12-5)/(4-0) = 7/4

so y = (7/4)x + 5

b) good grief, another abuse of equations and variables.
Just do the question!
cost = 3.2($2.50) + $6.90
= $14.90

a) To find the equation for the line that passes through the points (0,5) and (4,12), we can use the slope-intercept form of a linear equation:

y = mx + b

Where m is the slope of the line and b is the y-intercept.

First, let's find the slope (m). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

m = (y2 - y1) / (x2 - x1)

Plugging in the values: (x1, y1) = (0, 5) and (x2, y2) = (4, 12), we have:

m = (12 - 5) / (4 - 0)
= 7 / 4

Now that we have the slope, we can substitute it along with one of the given points into the slope-intercept form to find the y-intercept (b).

Using (x1, y1) = (0, 5):

5 = (7 / 4)(0) + b
5 = b

So the y-intercept (b) is 5.

Therefore, the equation for the line would be:

y = (7/4)x + 5

b) To calculate the fare without tips for a Yellow Cab ride from Como Park to the State Capitol, we need to establish a linear equation relating the fare to the distance traveled.

Let's assume that the distance traveled is represented by x (in miles) and the fare is represented by y (in dollars).

We know that the cab charges $6.90 for the time spent in the cab, regardless of the distance traveled. This is the y-intercept (b) of our linear equation.

We also know that they charge $2.50 per mile. This represents the slope (m) of our linear equation.

Therefore, the equation relating the fare (y) to the distance traveled (x) can be written as:

y = 2.50x + 6.90

To find the fare at the end for a 3.2 mile trek, we substitute x = 3.2 into the equation:

y = 2.50(3.2) + 6.90
y = 8 + 6.90
y = 14.90

Thus, the fare at the end, without tips, for a 3.2 mile trek would be $14.90.