Question

determine the slope for parts a, b, and c.
part a: a linear relationship is represented in the table.

x	-10	-5	0
y	2	5	8

determine the slope of the linear relationship. show every step of your work. (1 point)
part b: a line goes through the points (-10, 4) and (-7, -14). determine the slope of the line. show every step of your work. (1 point)
part c: a fish tank is leaking water. the tank starts with 120 liters of water and is leaking 3 liters of water each hour. determine the slope of the linear relationship. explain.
(2 points)

Explanation:

Part A

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Pick two table points

Use $(-10, 2)$ and $(-5, 5)$

Step3: Substitute values into formula

$m = \frac{5 - 2}{-5 - (-10)} = \frac{3}{5}$

Part B

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Identify given points

Use $(-10, 4)$ and $(-7, -14)$

Step3: Substitute values into formula

$m = \frac{-14 - 4}{-7 - (-10)} = \frac{-18}{3} = -6$

Part C

Step1: Define variables

Let $x$ = hours, $y$ = water volume

Step2: Identify slope meaning

Slope = rate of water change

Step3: Calculate slope

$m = \frac{\text{Change in } y}{\text{Change in } x} = \frac{-3}{1} = -3$
The negative sign means water volume decreases by 3 liters per hour.

Answer:

Part A: $\frac{3}{5}$
Part B: $-6$
Part C: $-3$; the slope represents the rate the tank loses water, decreasing by 3 liters each hour.