ANSWER
y = 2x - 1
EXPLANATION
We want to find the equation that represents the data in the table in the form:
y = mx + b
where m = slope
b = y intercept
To do this, we have to first find the slope of the equation using the formula for slope:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
where (x1, y1) and (x2, y2) are two sets of data points from the table.
Let us pick (0, -1) and (1, 1) as (x1, y1) and (x2, y2) respectively.
Therefore, the slope, m, is:
[tex]\begin{gathered} m=\frac{1-(-1)}{1-0}=\frac{1+1}{1}=\frac{2}{1} \\ m=2 \end{gathered}[/tex]
Now, we use the point-slope method to find the equation:
[tex]y-y1=m(x-x1)[/tex]
Therefore, the equation is:
[tex]\begin{gathered} y-(-1)=2(x-0) \\ y+1=2(x) \\ y+1=2x \\ y=2x-1 \end{gathered}[/tex]
That is the equation.
