Finding the equation in Standard Form.

Question

A High School basketball team scored 66 points from two-point baskets and three-point baskets. You wonder how many baskets of each type were made. Let x represent the number of two-point baskets and y represent the number of three-point baskets.

1) Create an equation to model the situation.

2) What is the x-intercept? What does it mean?

3) What is the y-intercept? What does it mean?

4) What is the slope?

Answer 1

2x + 3y = 66

3y = 66-2x

y = 22- (2/3)x y intercept = 22. It means that if there were only 3 pointers, then there were 22 of them.

2x= 66-3y

x= 33-(3/2)y x intercept = 33. It means if there were only 2 pointers then there were 33 of them.

If you plot x on the x axis and y on the y axis, the slope is -2/3. It's the coefficient of the x term, when the equation is solved for y. It's the change in y for a unit change in x. -2/3 means if there were 3 more 2 pointers there would be 2 less 3 pointers. It's an inverse relation, the more 2 pointers there were, the less 3 pointers there were.

This type of problem usually has an additional piece of information, such as how many total shots were taken, or some relation such as there were twice as many 2 pointers as 3 pointers. Then you could tell just how many of each shot were taken.