Question

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

x	y
3	-6
5	-12
7	-18

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 $(1, 0)$ and $(3, -6)$.
So, $m = \frac{-6 - 0}{3 - 1} = \frac{-6}{2} = -3$.

Step2: Find the y-intercept (b)

The slope - intercept form is $y = mx + b$. We know $m = -3$, and we can use the point $(1, 0)$ to find $b$.
Substitute $x = 1$, $y = 0$ and $m = -3$ into $y = mx + b$:
$0 = -3(1) + b$
$0 = -3 + b$
Add 3 to both sides: $b = 3$.

Step3: Write the equation

Now that we have $m = -3$ and $b = 3$, the slope - intercept form of the linear function is $y = -3x + 3$.

Answer:

$y = -3x + 3$