Solve the problem.
-A vendor has learned that, by pricing pretzels at $1.50, sales will reach 92 pretzels per day. Raising the price to $2.50 will cause the sales to fall to 48 pretzels per day. The number of pretzels, N, is a linear function of the
Price, x. Write a linear function that models the number of pretzels sold per day when the price is x dollars
Each.
A) N(x) = 44x + 26
C) N(x) = -44x + 158
D) N(x) = -44x - 158

Question

Solve the problem.
-A vendor has learned that, by pricing pretzels at $1.50, sales will reach 92 pretzels per day. Raising the price to $2.50 will cause the sales to fall to 48 pretzels per day. The number of pretzels, N, is a linear function of the
Price, x. Write a linear function that models the number of pretzels sold per day when the price is x dollars
Each.
A) N(x) = 44x + 26 
C) N(x) = -44x + 158 
D) N(x) = -44x - 158

Quizplus · Accepted Answer

To find the linear function that models the relationship between the price and the number of pretzels sold, we need to use the two given data points: (1.5, 92) and (2.5, 48). We can use the point-slope formula, which states:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the data points.

We can first find the slope of the line:

m = (y2 - y1) / (x2 - x1) 
m = (48 - 92) / (2.5 - 1.5) 
m = -44

Now we can use either of the two data points to find the equation of the line. Let's use (1.5, 92):

y - 92 = -44(x - 1.5)

Simplifying:

y = -44x + 158

Therefore, the linear function that models the relationship between the price and the number of pretzels sold is N(x) = -44x + 158. We can find the equation of the line using the two points (1.5, 92) and (2.5, 48) using the slope formula: 
slope = (48-92)/(2.5-1.5) = -44 
Using the point-slope formula, we get: 
N - 92 = -44(x - 1.5) 
N = -44x + 158 
Therefore, the correct choice is C.

Solve the Problem. -A Vendor Has Learned That, by Pricing Pretzels at $1.50