Question

if a table shows $x = 1, 2, 3$ and $y = 5, 3, 1$, what is the slope of the function?
\\(\circ\\) a. 1
\\(\circ\\) b. 2
\\(\circ\\) c. -1
\\(\circ\\) d. -2

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Select two points

We can take two points from the given \( x = [1, 2, 3] \) and \( y = [5, 3, 1] \). Let's take \((x_1,y_1)=(1,5)\) and \((x_2,y_2)=(2,3)\).

Step3: Calculate the slope

Substitute into the slope formula: \( m=\frac{3 - 5}{2 - 1}=\frac{-2}{1}=-2 \). We can also check with other points, say \((2,3)\) and \((3,1)\): \( m=\frac{1 - 3}{3 - 2}=\frac{-2}{1}=-2 \), which gives the same result.

Answer:

d. -2