Question

1. negative slopes

table 1:

x	y
1	10
2	8
3	6

table 2:

x	y
1	-2
2	-5
3	-8

a) calculate the slope of the function in table 1.
b) calculate the slope of the function in table 2.
c) explain what a negative slope indicates and compare the steepness of the two functions.

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope for Table 1

Let $(x_1,y_1)=(1,10)$ and $(x_2,y_2)=(2,8)$. Then $m_1=\frac{8 - 10}{2 - 1}=\frac{- 2}{1}=-2$.

Step3: Calculate slope for Table 2

Let $(x_1,y_1)=(1,-2)$ and $(x_2,y_2)=(2,-5)$. Then $m_2=\frac{-5-(-2)}{2 - 1}=\frac{-5 + 2}{1}=-3$.

Step4: Explain negative - slope and compare steepness

A negative slope indicates that as $x$ increases, $y$ decreases. The magnitude of the slope determines the steepness. Since $| - 3|>| - 2|$, the function in Table 2 is steeper than the function in Table 1.

Answer:

a) -2
b) -3
c) A negative slope means that as $x$ increases, $y$ decreases. The function in Table 2 is steeper than the function in Table 1 because $|-3| > |-2|$.