Question

Using function notation, create a linear function to represent scenario a. note: you will buy two admissions tickets (one for you and your friend). however, the number of drinks and snacks purchased are unknown.

Answer 1

To create a linear function to represent this scenario, we can let x represent the number of bus tickets purchased and y represent the number of burger purchases. From the given information, we know that Alphonso can afford 5 burgers if he spends all his money on burgers ($10/$2). This can be represented as the ordered pair (0, 5), where 0 represents the number of bus tickets purchased and 5 represents the number of burgers purchased. Similarly, if Alphonso spends all his money on bus tickets, he can afford 20 bus tickets ($10/$0.50). This can be represented as the ordered pair (20, 0), where 20 represents the number of bus tickets purchased and 0 represents the number of burgers purchased.

Step-by-step explanation:

To create a linear function to represent this scenario, we can let x represent the number of bus tickets purchased and y represent the number of burger purchases. From the given information, we know that Alphonso can afford 5 burgers if he spends all his money on burgers ($10/$2). This can be represented as the ordered pair (0, 5), where 0 represents the number of bus tickets purchased and 5 represents the number of burgers purchased. Similarly, if Alphonso spends all his money on bus tickets, he can afford 20 bus tickets ($10/$0.50). This can be represented as the ordered pair (20, 0), where 20 represents the number of bus tickets purchased and 0 represents the number of burgers purchased.

To find the linear function, we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By substituting the known points (0, 5) and (20, 0) into the equation, we can calculate the slope and y-intercept. Let's start with the slope:

m = (y2 - y1) / (x2 - x1)

m = (0 - 5) / (20 - 0)

m = -5/20 = -1/4

Now, let's find the y-intercept, b, by substituting one of the points into the equation:

5 = (-1/4)(0) + b

b = 5

Therefore, the linear function that represents this scenario is y = -1/4x + 5, where y represents the number of burger purchases and x represents the number of bus ticket purchases.