Question

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

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 $(1,0)$ and $(2,5)$. Then $m=\frac{5 - 0}{2 - 1}=5$.

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 $m = 5$ and we can use the point $(1,0)$. Substitute $x = 1$, $y=0$ and $m = 5$ into $y=mx + b$: $0=5\times1 + b$. Solving for $b$ gives $b=- 5$.

Answer:

$y = 5x-5$