Question

1. a sandwich shop uses a scale to ensure that each sandwich gets the same amount of deli meat. the graph shows the relationship between the number of sandwiches made, x, and the total weight of deli meat used, y, measured in ounces.

a. the point (4, 12) is shown. explain what information this point gives in the context of the problem.

b. if 18 ounces of meat are used, how many sandwiches can be made?

c. will the point (15, 42) be on the line that goes through these points? explain.

Explanation:

Step1: Interpret point (4, 12)

x = 4, y = 12 in context

Step2: Find number of sandwiches for 18 ounces of meat

Use ratio $\frac{y}{x}=3$, $x=\frac{18}{3}$

Step3: Check if (15, 42) is on the line

Find equation y = 3x, substitute x = 15, compare y values

Answer:

a. The point (4, 12) means that when 4 sandwiches are made, 12 ounces of deli - meat are used. In the context of the problem, x represents the number of sandwiches made and y represents the weight of deli - meat used in ounces. So for x = 4 sandwiches, y = 12 ounces of meat are used.
b. First, find the ratio of meat to sandwiches from the given points. If we assume the relationship is linear, from the point (4, 12), the ratio is $\frac{y}{x}=\frac{12}{4}=3$ ounces of meat per sandwich. If 18 ounces of meat are used, then the number of sandwiches made, x, can be found using the formula $x=\frac{y}{3}$. Substituting y = 18, we get $x=\frac{18}{3}=6$ sandwiches.
c. To check if the point (15, 42) is on the line, first find the equation of the line. Since the ratio of y to x (slope) is 3 (from part b), the equation of the line in slope - intercept form (y = mx + b, where b = 0 since when x = 0, y = 0) is y = 3x. Substitute x = 15 into the equation: y = 3×15=45. Since 45≠42, the point (15, 42) is not on the line.