Question

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

x | y
1 | 0
2 | 1
3 | 2
4 | 3

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

Explanation:

Step1: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$. Use $(x_1,y_1)=(1,0)$ and $(x_2,y_2)=(2,1)$:
$m=\frac{1-0}{2-1}=1$

Step2: Find y-intercept $b$

Use $y=mx+b$, substitute $m=1$, $x=1$, $y=0$:
$0=1(1)+b \implies b=0-1=-1$

Step3: Form linear equation

Substitute $m=1$ and $b=-1$ into $y=mx+b$:
$y=1x-1$ or $y=x-1$

Answer:

$y = x - 1$