Question

1. grid fluff and fold charges $2.25 for each load of laundry (lesson 1)

a. draw the graph of the proportional relationship between the two quantities, where x is the number of loads of laundry and y is the total cost.
laundry
graph with x-axis: number of loads (0-9), y-axis: total cost ($) (0-9)
b. describe how the unit rate is represented in the graph.

1. open response daniella makes apple pies each fall. the cost at the local grocery store for x pounds of apples is shown in the table. what is the least amount of money daniella will spend for 15 pounds of apples? assume the relationship is proportional. (lesson 1)

number of pounds, x	total cost ($), y
3	$6.75

1. multiple choice a turtle is crawling up a hill that rises 6 feet for every horizontal change of 36 feet. which of the following represents the slope of the hill, as a fraction in simplest form? (lesson 2)

a) 6/1 b) 1/6 c) 36/6 d) 6/36

1. open response the points in the table lie on a line. compute the slope of the line. (lesson 2)

x	y
-2	1
-4	2

1. multiselect which statement is true about the graph? select all that apply. (lesson 3)

graph with a line and two triangles

• the ratio of the rise to the run of each triangle is the same.
• the smaller triangle and the larger triangle shown are similar.
• the slope of the line is 2.
• the slope of the line is -2.
• the corresponding sides of the two triangles are not proportional.

module 4 • linear relationships and slope 249

Explanation:

Question 2 (Open Response: Daniella's Apple Pie Cost)

Step1: Find the unit rate (cost per pound)

From the table, for \( x = 2 \) pounds, \( y=\$4.50 \). The unit rate \( r \) is \( \frac{y}{x}=\frac{4.50}{2}=\$2.25 \) per pound.

Step2: Calculate cost for 15 pounds

Using the proportional relationship \( y = r\times x \), substitute \( r = 2.25 \) and \( x = 15 \). So \( y=2.25\times15 = 33.75 \).

Slope is defined as \( \text{slope}=\frac{\text{rise}}{\text{run}} \). Here, rise is 6 feet (vertical change) and run is 36 feet (horizontal change). So slope \(=\frac{6}{36}=\frac{1}{6}\) (simplified by dividing numerator and denominator by 6).

Step1: Recall the slope formula

Slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points, e.g., \( (6, - 3) \) and \( (-2,1) \).

Step2: Substitute into the formula

\( m=\frac{1-(-3)}{-2 - 6}=\frac{4}{-8}=-\frac{1}{2} \). (We can verify with another pair, e.g., \( (-2,1) \) and \( (-4,2) \): \( m=\frac{2 - 1}{-4-(-2)}=\frac{1}{-2}=-\frac{1}{2} \))

Answer:

\(\$33.75\)

Question 3 (Multiple Choice: Slope of the Hill)