Answer:
[tex]\displaystyle y=\frac{1}{2}x+6[/tex]
[tex]\displaystyle m=\frac{1}{2},\ b=6[/tex]
Step-by-step explanation:
Equation of a Line
Given two points through which a line passes, it's easy to find the equation of the line in the form
[tex]y=mx+b[/tex]
where m is the slope, and b is the y-intercept.
We are given the graph of the line and two clearly marked points to work with: (-4,4) (4,8)
We'll use the point-point formula to build the function of the line
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Plugging in the coordinates
[tex]\displaystyle y-4=\frac{8-4}{4-(-4)}(x-(-4))[/tex]
Operating
[tex]\displaystyle y-4=\frac{4}{8}(x+4)[/tex]
Simplifying
[tex]\displaystyle y-4=\frac{1}{2}(x+4)[/tex]
[tex]\displaystyle y-4=\frac{1}{2}x+2[/tex]
Rearranging
[tex]\displaystyle y=\frac{1}{2}x+2+4[/tex]
[tex]\displaystyle y=\frac{1}{2}x+6[/tex]
Here we can say
[tex]\displaystyle m=\frac{1}{2},\ b=6[/tex]
