Kathleen is ordering wraps from a local sandwich shop. The total charge includes a set delivery fee plus the price per wrap. Each wrap is the same price. Kathleen asks about specific orders and is given the following info:

If she orders 20 wraps, the total cost will be $100
If she orders 25 wraps, the total cost will be $122.50

Write a linear equation in the form y=mx+b to represent y, the total cost of ordering x sandwiches. Explain how you know your answer is correct. I'M SO LOST ON THIS ONE PLEASE HELP ME

c = a + b x

or
100 = a + b(20)
122.5 = a + b(25)
--------------------
22.5 = 5 b
b = 4.5

100 = a + 4.5*20
a = 10

so
y = 4.5 x + 10
-----------------
now check
if 25 wraps
y = 4.5*25 + 10 = 122.5 sure enough

THANK YOU SM PLZ CHECK MY OTHER MATH PROBLEMS I REALLY NEED HELP W THOSE :(

There is a limit to how many people I can help at once.

To write a linear equation in the form y = mx + b, we need to determine the values of m and b.

In this case, we can use the information given to find the values. We have two sets of data:

When Kathleen orders 20 wraps, the total cost is $100. This implies that the cost per wrap plus the delivery fee is $100. Therefore, we can write this as an equation: 20x + b =100.

Similarly, when Kathleen orders 25 wraps, the total cost is $122.50. Again, this implies that the cost per wrap plus the delivery fee is $122.50. We can write this as the second equation: 25x + b = 122.50.

Now, we have a system of two equations:
20x + b = 100 ---- (equation 1)
25x + b = 122.50 ---- (equation 2)

To solve this system of equations, we can subtract equation 1 from equation 2:
25x + b - (20x + b) = 122.50 - 100
Simplifying, we get:
5x = 22.50

Dividing both sides by 5, we find:
x = 4.50

Now, we can substitute this value back into one of the original equations, equation 1 for example, to find the value of b:
20 * 4.50 + b = 100
90 + b = 100
b = 10

Therefore, the linear equation in the form y = mx + b is:
y = 4.50x + 10

To confirm that this equation is correct, let's check one of the given examples:
If Kathleen orders 20 wraps (x = 20), the total cost should be $100 (y = 100).
When we substitute these values into the equation, we get:
y = 4.50 * 20 + 10 = 90 + 10 = 100

Since the equation yields the correct result, we can conclude that the linear equation is accurate.