The equation of a line in its slope intercept form is given by:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
We know that the y-intercept is the value of y when x=0, hence from the table we have that b=-2.
To find the slope we use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plugging the first two points on the table we have:
[tex]\begin{gathered} m=\frac{8-(-2)}{1-0} \\ m=\frac{8+2}{1} \\ m=\frac{10}{1} \\ m=10 \end{gathered}[/tex]
Once we know the slope and y-intercept we plug them in the equation above, therefore the equation we are looking for is:
[tex]y=10x-2[/tex]
