Question

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

x	y
-	-
1	10
2	24
3	38
4	52

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 $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(1,10)$ and $(2,24)$: $m=\frac{24 - 10}{2 - 1}=\frac{14}{1}=14$.

Step2: Find the y - intercept

The equation of a line is $y=mx + b$. Substitute $m = 14$, $x = 1$ and $y = 10$ into the equation: $10=14\times1 + b$. Solving for $b$ gives $b=10 - 14=- 4$.

Answer:

$y = 14x-4$