Question

given the table below, write a linear equation that defines the dependent variable, y, in terms of the independent variable, x.
show your work here
given the table below, write a linear equation that defines the dependent variable, y, in terms of the independent variable, x.

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 from the first - table, say $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(3,2)$. Then $m=\frac{2 - 1}{3-0}=\frac{1}{3}$.

Step2: Find the y - intercept (b)

The linear equation is in the form $y=mx + b$. When $x = 0$, $y=b$. From the first table, when $x = 0$, $y = 1$, so $b = 1$. The linear equation for the first table is $y=\frac{1}{3}x+1$.

Step3: For the second table

Let $(x_1,y_1)=(3,17)$ and $(x_2,y_2)=(6,16)$. Then $m=\frac{16 - 17}{6 - 3}=-\frac{1}{3}$.

Step4: Find the y - intercept for the second table

Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(3,17)$ and $m=-\frac{1}{3}$.
$y-17=-\frac{1}{3}(x - 3)$
$y-17=-\frac{1}{3}x + 1$
$y=-\frac{1}{3}x+18$

Answer:

For the first table: $y=\frac{1}{3}x + 1$; For the second table: $y=-\frac{1}{3}x+18$