Question

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

x	y
1	-1
2	2
3	5
4	8

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the points $(1,-1)$ and $(2,2)$. Then $m=\frac{2-(-1)}{2 - 1}=\frac{2 + 1}{1}=3$.

Step2: Find the y - intercept

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know $m = 3$, and we can use a point from the table, say $(1,-1)$. Substitute $x = 1$, $y=-1$ and $m = 3$ into $y=mx + b$: $-1=3\times1 + b$. Solving for $b$ gives $b=-1-3=-4$.

Answer:

$y = 3x-4$