Question

find the equation of the linear function represented by the table below in slope-intercept form. \

$$\begin{tabular}{|c|c|} \\hline $x$ & $y$ \\\\ \\hline $-1$ & $5$ \\\\ \\hline $3$ & $1$ \\\\ \\hline $7$ & $-3$ \\\\ \\hline $11$ & $-7$ \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's use the points $(-1, 5)$ and $(3, 1)$.
So, $m = \frac{1 - 5}{3 - (-1)} = \frac{-4}{4} = -1$.

Step2: Find the y-intercept (b)

Use the slope-intercept form $y = mx + b$ and one of the points, say $(-1, 5)$ with $m = -1$.
Substitute $x = -1$, $y = 5$, and $m = -1$ into the equation:
$5 = -1\times(-1) + b$
$5 = 1 + b$
Subtract 1 from both sides: $b = 5 - 1 = 4$.

Step3: Write the equation

Now that we have $m = -1$ and $b = 4$, the slope-intercept form is $y = -x + 4$.

Answer:

$y = -x + 4$