Question

1. caroline used a pump to remove water from a pond. the pump removes 300 gallons of water per hour. on saturday, she used the pump to remove 450 gallons. she continued to use the pump on sunday. write the equation of the line that represents the relationship between the total amount of water (y), in gallons, caroline removed from the pond over the weekend after using the pump for x hours on sunday?
2. the table shows values of y as a function of x. write the equation that describes the linear relationship shown in the table of values.

x	45	60	75
y	8	9	10

1. what is the slope to the line $6x - 3y = 12$?

17
a. what is the slope of a line parallel to the given line?

Explanation:

Question 14

Step1: Identify the slope and y-intercept

The pump removes 300 gallons per hour, so the slope \( m = 300 \). On Saturday, 450 gallons were removed, so the y-intercept (initial amount on Sunday) \( b = 450 \).

Step2: Use the slope - intercept form

The slope - intercept form of a line is \( y=mx + b \). Substituting \( m = 300 \) and \( b = 450 \), we get \( y=300x + 450 \).

Step1: Calculate the slope

Using two points, say \( (45,8) \) and \( (60,9) \). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{9 - 8}{60 - 45}=\frac{1}{15} \).

Step2: Use point - slope form

Using the point \( (45,8) \) and \( m=\frac{1}{15} \). The point - slope form is \( y - y_1=m(x - x_1) \). So \( y - 8=\frac{1}{15}(x - 45) \). Simplifying, \( y-8=\frac{1}{15}x - 3 \), then \( y=\frac{1}{15}x+5 \).

Step1: Rewrite the equation in slope - intercept form

Start with \( 6x-3y = 12 \). Subtract \( 6x \) from both sides: \( - 3y=-6x + 12 \). Divide both sides by - 3: \( y = 2x-4 \).

Step2: Identify the slope

In the slope - intercept form \( y=mx + b \), the slope \( m = 2 \).

Answer:

\( y = 300x+450 \)

Question 15