Question

lo: swbat represent linear relationships using multiple representations. dol: given a set of problems, students will correctly represent linear relationships using multiple representations in at least 4 of 5 questions. 1. a water tank is being drained at a constant rate of 20 gallons per minute. the tank initially contains 150 gallons of water. which equation represents the amount of water, g, in the tank after t minutes? a. t = -20g + 150 b. g = 20t + 150 c. g = -20t + 150 d. t = 20g + 150 2. which equation represents the relationship between the independent and dependent variables? x: 0, 3, 5, 6, 9 y: -1, -16, -26, -31, -46 a. y = -5x - 1 b. y = 15x - 1 c. y = -5x + 5 d. y = -x - 5 3. a new music streaming service charges a monthly membership fee plus an additional cost for each album downloaded. the total cost, c, in dollars can be represented by the equation c = 1.50a + 5, where a is the number of albums downloaded. which of the following ordered pairs (a, c) would not be on the graph representing this relationship? a. (0, 5) b. (2, 8) c. (3, 9) d. (4, 11)

Explanation:

1.

Step1: Identify the rate and initial - value

The water is drained at a rate of 20 gallons per minute (negative rate since the amount of water is decreasing), and the initial amount of water is 150 gallons. The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, $m=-20$ and $b = 150$, and the amount of water $g$ is a function of time $t$. So the equation is $g=-20t + 150$.

Step1: Find the slope

The slope $m=\frac{\Delta y}{\Delta x}$. Using the points $(0,-1)$ and $(3,-16)$, $m=\frac{-16-(-1)}{3 - 0}=\frac{-16 + 1}{3}=\frac{-15}{3}=-5$.

Step2: Find the y - intercept

When $x = 0$, $y=-1$, so the y - intercept $b=-1$. The linear equation is $y=-5x-1$.

Step1: Substitute the values of $a$ into the equation $c = 1.5a+5$

For option A: When $a = 0$, $c=1.5\times0 + 5=5$, so $(0,5)$ is on the graph.
For option B: When $a = 2$, $c=1.5\times2+5=3 + 5=8$, so $(2,8)$ is on the graph.
For option C: When $a = 3$, $c=1.5\times3+5=4.5 + 5=9.5
eq9$, so $(3,9)$ is not on the graph.
For option D: When $a = 4$, $c=1.5\times4+5=6 + 5=11$, so $(4,11)$ is on the graph.

Answer:

C. $g=-20t + 150$

2.