Question

#11: During a basketball game the Dragons made 12 three

pointers and 11 foul shots (1 point each) and the rest of their
points came from two point baskets.
Determine the equation, slope and y-intercept for a function
that outputs the total points the Dragons scored (p) based on
the number of 2-point baskets made (b).
Slope:
Y-Intercept:
Equation (in slope-intercept form):

Answer 1

The function to determine the total points scored by the Dragons is p = 2b + 47, where 'b' represents the number of two-point baskets made. The slope of the function is 2, signifying that each 2-point basket adds 2 points to the total score. The y-intercept is 47, reflecting the points scored from three-pointers and foul shots.

Step-by-step explanation:

To determine the equation of the function that represents the total points the Dragons scored (p) based on the number of 2-point baskets made (b), let's consider the points contributed by three-pointers and foul shots. The Dragons made 12 three-pointers worth 3 points each and 11 foul shots worth 1 point each, thus contributing a fixed number of points regardless of the two-point baskets.

The points from three-pointers and foul shots are calculated as follows:
Three-pointers: 12 × 3 = 36 points
Foul shots: 11 × 1 = 11 points
The fixed points are therefore 36 + 11 = 47 points.

Each two-point basket made contributes 2 points to the score. Therefore, the total points (p) can be calculated by the equation: p = 2b + 47.

The slope (m) of this function is 2, since that is the coefficient of the variable b in the equation. The y-intercept (b) is 47, which represents the fixed points scored from three-pointers and foul shots. The linear equation in slope-intercept form is p = 2b + 47, where p is the total points scored and b is the number of two-point baskets.

Answer 2

Slope: 2

Y-Intercept: 47

Equation (in slope-intercept form): p = 2b + 47.

Step-by-step explanation:

To determine the equation, slope, and y-intercept for a function that outputs the total points the Dragons scored based on the number of 2-point baskets made, you will need to use the information given about the number of 3-pointers, foul shots, and 2-point baskets made.

First, let's define p as the total number of points the Dragons scored and b as the number of 2-point baskets made.

We know that the Dragons scored a total of 12 three-pointers * 3 points per 3-pointer + 11 foul shots * 1 point per foul shot = 47 points from 3-pointers and foul shots.

Therefore, the total number of points the Dragons scored can be expressed as:

p = 47 points + 2 points per 2-point basket * b 2-point baskets

This equation is in slope-intercept form, with the slope being 2 points per 2-point basket and the y-intercept being 39 points.

The equation in slope-intercept form is:

p = 2b + 47

Therefore, the slope of the function is 2, the y-intercept is 39, and the equation is p = 2b + 47.