Question

this question has two parts. first, answer part a. then, answer part b.
part a
reasoning shikita borrowed money from her brother and paid back a set amount each week. the table shows how much she owed in a given week.

week	3	6	8	10	13
amount owed	$32.50	$25.00	$20.00	$15.00	$7.50

a. let x represent the number of weeks and y represent the amount owed. write an equation in slope - intercept form to model the amount shikita owed each week.
part b
b. describe the graph of the equation you found in part a. what does its shape tell you about the problem?
it is a select choice. this means that the amount shikita owes select choice by select choice amount each week.

Explanation:

Part A

Step 1: Find the slope (m)

We use two points from the table, say \((x_1, y_1) = (3, 32.50)\) and \((x_2, y_2) = (6, 25.00)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m=\frac{25.00 - 32.50}{6 - 3}=\frac{-7.50}{3}=-2.5\)

Step 2: Find the y - intercept (b)

Use the slope - intercept form \(y = mx + b\) and one of the points, e.g., \((x = 3,y = 32.50)\) and \(m=-2.5\).
Substitute into the equation: \(32.50=-2.5\times3 + b\)
\(32.50=-7.5 + b\)
Add 7.5 to both sides: \(b=32.50 + 7.5=40\)

Step 3: Write the equation

The slope - intercept form is \(y=mx + b\). Substituting \(m = - 2.5\) and \(b = 40\), we get \(y=-2.5x + 40\) (or \(y =-\frac{5}{2}x+40\))

The equation \(y=-2.5x + 40\) is a linear equation in the form \(y = mx + b\) where \(m=-2.5\) (negative) and \(b = 40\). The graph of a linear equation of the form \(y=mx + b\) is a straight line. Since the slope \(m=-2.5\) is negative, the line is decreasing. A negative slope in this context means that as the number of weeks (\(x\)) increases, the amount owed (\(y\)) decreases. The "shape" (a straight line) tells us that the amount Shikita owes changes at a constant rate (since linear functions have a constant rate of change) each week. The rate of change is \(- 2.5\) dollars per week, which means she pays back \(2.5\) dollars each week.

For the fill - in - the - blanks:

• It is a "straight line".
• This means that the amount Shikita owes "decreases" by "a constant" amount each week.

Answer:

\(y=-2.5x + 40\) (or \(y =-\frac{5}{2}x + 40\))

Part B