Question

write the linear equation that gives the rule for this table.

x	y
3	2
4	3
5	4

write your answer as an equation with y first, followed by an equals sign.

Explanation:

Step1: Find the slope

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

Step2: Find the y - intercept

The equation of a line is $y=mx + b$. We know $m = 1$. Using the point $(2,1)$ and substituting into $y=mx + b$, we get $1=1\times2 + b$. Solving for $b$: $b=1 - 2=-1$.

Step3: Write the equation

The equation of the line is $y=mx + b$. Substituting $m = 1$ and $b=-1$, we have $y=x - 1$.

Answer:

$y=x - 1$