write the linear equation that gives the rule for this table. write your answer as an equation with y first…

Explanation:

Step1: Find the slope

The slope $m$ of a line is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(x_1,y_1)=(1,0)$ and $(x_2,y_2)=(2,1)$. Then $m=\frac{1 - 0}{2 - 1}=1$.

Step2: Find the y - intercept

The equation of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Substitute $m = 1$, and the point $(x,y)=(1,0)$ into the equation: $0=1\times1 + b$. Solving for $b$, we get $b=- 1$.

Step3: Write the equation

Substitute $m = 1$ and $b=-1$ into $y=mx + b$. The equation is $y=x - 1$.

Answer:

$y=x - 1$