Question

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

x	y
1	0
3	8
5	16

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 $(-1, -8)$ and $(1, 0)$.
So, $m = \frac{0 - (-8)}{1 - (-1)} = \frac{8}{2} = 4$.

Step2: Find the y-intercept (b)

The slope-intercept form is $y = mx + b$. We know $m = 4$, and we can use the point $(1, 0)$ to solve for $b$.
Substitute $x = 1$, $y = 0$, and $m = 4$ into the equation: $0 = 4(1) + b$.
Simplify: $0 = 4 + b$, so $b = -4$.

Step3: Write the equation

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

Answer:

$y = 4x - 4$