The equation of a line in slope intercept form is:
[tex]y=mx+b[/tex]
where m is the slope and b is the y intercept.
In this case we notice that the y-intercept is 2, this means that b=2.
To find the slope we need to use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
using the points (0,2) and (8,0). We have that the slope is:
[tex]\begin{gathered} m=\frac{0-2}{8-0} \\ =-\frac{2}{8} \\ =-\frac{1}{4} \end{gathered}[/tex]
Now we plug the values for the slope and the intercept in the equation, therefore the equation we are looking for is:
[tex]y=-\frac{1}{4}x+2[/tex]
