Question

name: santiago c
period 3rd
7th math - homework week 22

1. a streaming service charges a monthly membership fee of $10.00 plus a rental fee of $2.50 per movie watched. write an equation in slope - intercept form y = mx + b that represents the total cost, y, for a month where x movies are watched.
2. the table below shows the height of a burning candle over time.

time in hours (x)	0	2	4	6

a. does this table represent a proportional or non - proportional linear relationship?
b. what is the rate of change (slope) of the line?

Explanation:

Problem 1: Streaming Service Cost Equation

Step1: Identify slope and intercept

The monthly membership fee is the y - intercept ($b = 10$) and the rental fee per movie is the slope ($m = 2.50$).

Step2: Write slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substituting $m = 2.50$ and $b = 10$ into the formula, we get $y = 2.5x+10$.

For a proportional relationship, the equation should be in the form $y = kx$ (where $k$ is the constant of proportionality) and when $x = 0$, $y$ should be 0. From the table, when $x = 0$ (time = 0 hours), $y=20$ (height = 20 cm). Since $y
eq0$ when $x = 0$, it does not pass through the origin. So, it is a non - proportional linear relationship.

Step1: Use slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(x_1,y_1)=(0,20)$ and $(x_2,y_2)=(2,16)$.

Step2: Calculate the slope

Substitute the values into the slope formula: $m=\frac{16 - 20}{2 - 0}=\frac{- 4}{2}=-2$. We can check with other points, e.g., $(2,16)$ and $(4,12)$: $m=\frac{12 - 16}{4 - 2}=\frac{-4}{2}=-2$, and $(4,12)$ and $(6,8)$: $m=\frac{8 - 12}{6 - 4}=\frac{-4}{2}=-2$.

Answer:

$y = 2.5x + 10$

Problem 2A: Proportional or Non - proportional