Question

the table shows a linear relationship between x and y. x y -6 -1 0 -3 3 -4 9 -6 create an equation that describes the relationship shown in the table. move the correct answer to each box. not all answers will be used.

Explanation:

Step1: Find the slope (m)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(x_1,y_1)=(0, - 3)$ and $(x_2,y_2)=(3,-4)$. Then $m=\frac{-4-(-3)}{3 - 0}=\frac{-4 + 3}{3}=\frac{-1}{3}=-\frac{1}{3}$.

Step2: Find the y - intercept (b)

The y - intercept is the value of y when x = 0. From the table, when x = 0, y=-3, so b=-3.

Step3: Write the linear equation

The slope - intercept form of a linear equation is $y=mx + b$. Substituting $m =-\frac{1}{3}$ and b=-3, we get $y=-\frac{1}{3}x-3$.

Answer:

$y =-\frac{1}{3}x-3$