Question

Natalia and her friends held a bake sale to benefit a local charity. The friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale. They collected $60 on the first day and $88 on the second day. Write an equation to represent the amount R Natalia and her friends raised after selling c cakes.

The name of the assignment is 5-1 Writing Equations In Slope Intercept Form

Answer 1

✅
`R = 4c`

Explanation:

The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as
`y = mx + b`.

Where,

y = R (amount of cake sold in dollars)

x = c (cakes sold)

m = slope

b = y-intercept.

The equation would look like:

`R = mc + b`

We need to find the value of m and b, to get an equation to represent the situation.

The first point we have from the information given is (15, 60) => 15 cakes sold for $60.

The second point is (22, 88) => 22 cakes sold for $88.

`slope (m) = (y_2 - y_1)/(x_2 - x_1) = (88 - 60)/(22 - 15) = (28)/(7) = 4`

To find b, substitute c = 15, R = 60 and m = 4, into
`R = mc + b`.

`60 = 4(15) + b`

`60 = 60 + b`

`0 = b`

Since b = 0, this means there is a proportional relationship between R and c.

Substitute m = 4 and b = 0 into
`R = mc + b` to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.

`R = 4c + 0`

✅
`R = 4c`