Question

You lose track of how many 2-point baskets and 3-point baskets a team makes in a basketball game. The team misses all the 1-point baskets and still scores 54 points. The equation 2x+3y=54$ models the total points scored, where x is the number of 2-point baskets made and y is the number of 3-point baskets made. a. Find and interpret the intercepts.

Answer 1

• x-intercept: 27, the number of 2-pointers if no 3-pointers
• y-intercept: 18, the number of 3-pointers if no 2-pointers

Explanation:

Each intercept is found by setting the other variable to zero and solving for the variable value of interest.

2x +3y = 54

x-intercept:

2x = 54

x = 27

y-intercept:

3y = 54

y = 18

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By definition, the intercept values are the values that satisfy the equation when the other variable is zero.

x-intercept: To score 54 points, the team would have to make 27 2-point baskets if no 3-point baskets were made.

y-intercept: To score 54 points, the team would have to make 18 3-point baskets if no 2-point baskets were made.