Question

After the booster club sold 40 hot dogs at a football game, it had $90 in profit. After the next game, it had sold a total of 80 hot dogs and had a total of $210 in profit. Which equation models the total profit,y,based on the number of hotdogs sold,x

Answer 1

The equation that models the total profit based on the number of hot dogs is y = 3x - 30.

Step-by-step explanation:

The equation that models the total profit based on the number of hot dogs sold is:

y = mx + b

Where:

• y represents the total profit
• x represents the number of hot dogs sold
• m represents the slope of the line (change in profit per hot dog sold)
• b represents the y-intercept (initial profit when no hot dogs are sold)

To find the values of m and b, we use the information given in the question. We have two points on the line: (40, 90) and (80, 210). We can use these points to find the slope and the y-intercept.

Slope (m) = (change in profit) / (change in hot dogs sold) = (210 - 90) / (80 - 40) = 120 / 40 = 3

Substituting the values of m and one of the points into the equation, we can solve for b:

90 = 3(40) + b

b = 90 - 120 = -30

Therefore, the equation that models the total profit is y = 3x - 30.

Answer 2

The correct answer would be: y-90=3(x-40)