Question

what is the function rule for the linear function in this table?

slope-intercept form
\\(y = mx + b\\)

\\(\

$$\begin{array}{|c|c|c|c|c|}\\hline \\text{input } (x) & 0 & 1 & 2 & 3 \\\\ \\hline \\text{output } (y) & 5 & 3 & 1 & -1 \\\\ \\hline \\end{array}$$

\\)

\\(y = ?x + \square\\)

Explanation:

Identify the y-intercept

The y-intercept \(b\) is the value of \(y\) when \(x = 0\). Looking at the table, when \(x = 0\), \(y = 5\). Thus, \(b = 5\).

Calculate the slope

The slope \(m\) is the rate of change of \(y\) with respect to \(x\). Using the points \((0, 5)\) and \((1, 3)\):

$$ m = \frac{3 - 5}{1 - 0} = -2 $$

Write the function rule

Substitute \(m = -2\) and \(b = 5\) into the slope-intercept form \(y = mx + b\):

$$ y = -2x + 5 $$

Answer:

What is the function rule for the linear function in this table?

\(y =\) <blank>\(-2\)</blank>\(x +\) <blank>\(5\)</blank>