Answer:
✅[tex] R = 4c [/tex]
Step-by-step explanation:
The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as [tex] y = mx + b [/tex].
Where,
y = R (amount of cake sold in dollars)
x = c (cakes sold)
m = slope
b = y-intercept.
The equation would look like:
[tex] R = mc + b [/tex]
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.
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{88 - 60}{22 - 15} = \frac{28}{7} = 4 [/tex]
To find b, substitute c = 15, R = 60 and m = 4, into [tex] R = mc + b [/tex].
[tex] 60 = 4(15) + b [/tex]
[tex] 60 = 60 + b [/tex]
[tex] 0 = b [/tex]
Since b = 0, this means there is a proportional relationship between R and c.
Substitute m = 4 and b = 0 into [tex] R = mc + b [/tex] to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.
[tex] R = 4c + 0 [/tex]
✅[tex] R = 4c [/tex]
