The line passing through two points that are
[tex](x_1,y_1_{})=(4,8),\text{ }(x_2,y_2)=(-4,6)[/tex]
Part (a)
The formula for the slope of a line is given below
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-8}{-4-4}=\frac{-2}{-8}=\frac{1}{4}[/tex]
Therefore, the slope of the line is 1/4.
Part (b)
The point-slope form of a line given by the formula
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the values and find the equation of the line as follows
[tex]y-4=\frac{1}{4}(x-8)[/tex]
Part (c)
The slope-intercept form of a line has the general form of
[tex]y=mx+c[/tex]
Now, manipulate the equation in part (b) to convert it into the above form as follows
[tex]\begin{gathered} y-4=\frac{1}{4}(x-8) \\ \Rightarrow4y-16=x-8 \\ \Rightarrow4y=x+8 \\ \Rightarrow y=\frac{1}{4}x+2 \end{gathered}[/tex]
