Question

1. the boys basketball team has a storage closet that they store basketballs in when they are not in use. the amount of space decreases by 2 feet per basket ball placed in the closet. currently there are 5 basketballs in the storage closet with 10 square feet of area left. write an equation that shows the amount of square footage remaining in the container, y, as a function of the amount of basketballs placed in the container, x.

1. the point (3, 2) is on the line $y = 2x + b$. find the value of b.

Explanation:

Step1 (Problem 4): Identify slope and given point

Slope $m = -2$, point $(x_1,y_1)=(5,10)$

Step2 (Problem 4): Use point-slope form

$y - y_1 = m(x - x_1)$
$y - 10 = -2(x - 5)$

Step3 (Problem 4): Simplify to slope-intercept

$y - 10 = -2x + 10$
$y = -2x + 20$

Step1 (Problem 5): Substitute point into line equation

$x=3$, $y=2$, so $2 = 2(3) + b$

Step2 (Problem 5): Solve for b

$2 = 6 + b$
$b = 2 - 6$

Answer:

1. $y = -2x + 20$
2. $b = -4$