The slope intercept form is:
[tex]y=mx+b[/tex]
Where is [tex]m[/tex] the slope of the line and [tex]b[/tex] the intercept with the y-axis.
To find the slope, take any two points from the table provided. For example:
(1, 1/5)
(3, 1)
So:
[tex]m = \frac{1- 1/5}{3-1}[/tex]
[tex]m = \frac{2}{5}[/tex]
Now we find b substituting any point of the table in the equation:
[tex]y_0 = \frac{2}{5}x_0 + b[/tex]
We substitute the poiunt (3, 1) for example:
[tex]1 = \frac{2}{5}(3) + b[/tex]
Now we solve for b:
[tex]b = 1 -\frac{6}{5}\\\\b = -\frac{1}{5}[/tex]
Finally, the equation is:
[tex]y = \frac{2}{5}x -\frac{1}{5}[/tex]
The answer is the last option
