Question

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

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline -1 & 5 \\\\ \\hline 2 & -4 \\\\ \\hline 5 & -13 \\\\ \\hline 8 & -22 \\\\ \\hline \\end{array}$$

\\)

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(-1, 5)$ and $(2, -4)$.
So, $m = \frac{-4 - 5}{2 - (-1)} = \frac{-9}{3} = -3$.

Step2: Find the y-intercept (b)

The slope - intercept form is $y = mx + b$. We can use one of the points and the slope we found. Let's use the point $(-1, 5)$ and $m=-3$.
Substitute into the equation: $5 = -3\times(-1)+b$.
Simplify: $5 = 3 + b$.
Subtract 3 from both sides: $b = 5 - 3 = 2$.

Step3: Write the equation

Now that we have $m = -3$ and $b = 2$, the equation in slope - intercept form is $y=-3x + 2$.

Answer:

$y = - 3x+2$