Question

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

x	y
1	-4
2	-8
3	-12

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 the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,0)$ and $(1, - 4)$, we have $m=\frac{-4 - 0}{1 - 0}=-4$.

Step2: Find the y - intercept

The y - intercept $b$ is the value of $y$ when $x = 0$. From the table, when $x = 0$, $y = 0$, so $b = 0$.

Step3: Write the linear equation

The slope - intercept form of a linear equation is $y=mx + b$. Substituting $m=-4$ and $b = 0$ into the equation, we get $y=-4x+0$, which simplifies to $y=-4x$.

Answer:

$y=-4x$