Question

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

x	y
2	53
3	54
4	55

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 $(x_1,y_1)=(1,52)$ and $(x_2,y_2)=(2,53)$. Then $m=\frac{53 - 52}{2 - 1}=1$.

Step2: Find the y - intercept

The equation of a line is $y=mx + b$. Substitute $m = 1$, $x = 1$ and $y = 52$ into the equation: $52=1\times1 + b$. Solving for $b$, we get $b=52 - 1=51$.

Step3: Write the equation

The linear equation is $y=1x+51$ or simply $y=x + 51$.

Answer:

$y=x + 51$