Question

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

x	y
1	3
2	4
3	5
4	6

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1,3)$ and $(x_2,y_2)=(2,4)$. Then $m=\frac{4 - 3}{2 - 1}=1$.

Step2: Find the y - intercept

The slope - intercept form is $y=mx + b$. Substitute $m = 1$, $x = 1$ and $y = 3$ into the equation: $3=1\times1 + b$. Solving for $b$ gives $b=3 - 1=2$.

Step3: Write the equation

The equation of the line in slope - intercept form is $y=mx + b$. Substituting $m = 1$ and $b = 2$ we get $y=x + 2$.

Answer:

$y=x + 2$