Having compared the functions of both conditions, from Mr. Baker and his competition, it is correct to see that: "Both functions have different slopes and intercepts" (Option B).
To prove the above, first we need to derive the equation of the function of Mr. Baker in slope - intercept form:
y = mx + b
We need to determine the values of m (slope) and b (the y-intercept).
First, lets us compute the slope (m):
m = Δ in Y/ Δ in x
m = (608 - 572) / 36/3
m = 12
Thus, inserting the values for the equation, we have:
572 = 12 * 0 + b
b = 572
Thus,
y = 12x + 572
Part II - now we compare both functions:
Since we have:
1) f(x) = 12x + 572 - which indicates Mr. Bakers total monthly profit; and
2) g(x) = 10x + 72 - which indicates Waxy Business's total profit,
we can see clearly that the two functions have different slopes and intercepts.
Slope for Mr. Baker's function is 12 while that of his competition is 10
The intercept of Mr. Baker's function is 572 while that of his competition is 72.
Full Question:
Although part of your question is missing, you might be referring to this full question:
Mr. Baker sells boxes of votive candles to stores. He also has a customer who places a fixed order for a designer candle every month. Mr. Baker’s total monthly profit from selling votive candles and his fixed order is shown in the table, where x is the number of boxes of votive candles he sells:
Number of Boxes of Votive Candles (x) | Total Monthly Profit
------------------------------------|--------------------
0 | 572
1 | 584
2 | 596
3 | 108
Part A: Write an equation in slope-intercept form for the function represented in the table:
Function: y = mx + b
Part C:
Mr. Baker’s competitor, Waxy Business, also sells candles. The competitor’s total profit from selling boxed votive candles and fixed orders of designer candles is represented by the function g(x) = 10x + 72. Compare the two functions using their key features. (Note: you might wish to graph the functions to compare them.)
a) Both functions have the same slope but different intercepts.
b) Both functions have different slopes and intercepts.
c) Both functions have the same intercept but different slopes.
d) Both functions have the same slope and intercept.