Question

1. bob works for the local aquarium where he is in charge of cleaning out the fish tanks. he must drain the fish tank before he can inspect and clean it. the tank can drain 45 gallons of water every 5 hours. the tank currently contains 288 gallons of water.

write a linear equation, for bob, to represent how long it will take to drain the fish tank before he can clean it. let ( g(x) ) represent the number of gallons remining for after a given number of hours, ( x ).

hours, ( x )	gallons, ( g(x) )
5	243
10	198
20	108

1. the scatter plot below shows the linear trend of the number of golf carts a company sold in the month of february and a line of best fit representing this trend.

part a:
what is the meaning of the slope as a rate of change for this line of best fit?

part b:
what is the meaning of the ( y )-intercept for this line of best fit?

(scatter plot for problem 14: golf cart sales, x-axis: days (3, 6, 9, 12, 15, 18, 21, 24, 27), y-axis: golf carts sold (10, 20, 30, 40, 50, 60, 70, 80, 90))

Explanation:

Question 13 (Linear Equation for Draining Tank)

Step1: Find the rate of drainage

The tank drains 45 gallons every 5 hours, so the rate (slope) is $\frac{45}{5} = 9$ gallons per hour. But since it's draining, the slope is -9.

Step2: Identify the initial amount (y-intercept)

The tank initially has 288 gallons, so the y-intercept \( b = 288 \).

Step3: Write the linear equation

Using the slope-intercept form \( G(x) = mx + b \), where \( m = -9 \) and \( b = 288 \), we get \( G(x) = -9x + 288 \).

The slope of the line of best fit represents the rate of change of golf carts sold per day. From the graph, as days increase, golf carts sold decrease. Calculating slope: using points (0, 90) and (18, 0), slope \( m=\frac{0 - 90}{18 - 0}=-5 \). So the slope means the company sells 5 fewer golf carts per day.

The y - intercept is the value when \( x = 0 \) (days = 0, start of February). From the line of best fit, when \( x = 0 \), \( y = 90 \). So it represents the estimated number of golf carts sold on day 0 (start of February), which is 90.

Answer:

\( G(x) = -9x + 288 \)

Question 14 Part A (Slope Meaning)