Answer:
Third option: [tex]y= \frac{1}{4}x+2[/tex]
Step-by-step explanation:
The correct form of the exercise is: "The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is [tex]y -4 = \frac{1}{4}(x -8)[/tex]. What is the slope-intercept form of the equation for this line?"
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the equation of the line in Point-Slope form:
[tex]y -4 = \frac{1}{4}(x -8)[/tex]
You need to solve for "y" in order to write the given equation of the line in Slope Intercept form.
Then, this is:
[tex]y -4 = \frac{1}{4}(x -8)\\\\y-4= \frac{1}{4}x-\frac{8}{4}\\\\y-4= \frac{1}{4}x-2\\\\y= \frac{1}{4}x-2+4\\\\y= \frac{1}{4}x+2[/tex]
You can identify that the slope "m" is:
[tex]m=\frac{1}{4}[/tex]
And the y-interecept "b" is:
[tex]b=2[/tex]
