To determine the equation of the line, given that you know the slope and the coordinates of one point, you can use the point-slope form, which is:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of the point
Replace the values in the equation
m=-1/8
(x₁,y₁)= (4,4)
[tex]y-4=-\frac{1}{8}(x-4)[/tex]Next, write the equation in slope-intercept form:
-Distribute the multiplication in the parentheses term
[tex]\begin{gathered} y-4=-\frac{1}{8}\cdot x-(-\frac{1}{8})\cdot4 \\ y-4=-\frac{1}{8}x-(-\frac{1}{2}) \\ y-4=-\frac{1}{8}x+\frac{1}{2} \end{gathered}[/tex]-Add 4 to both sides of the expression
[tex]\begin{gathered} y-4+4=-\frac{1}{8}x+\frac{1}{2}+4 \\ y=-\frac{1}{8}x+\frac{9}{2} \end{gathered}[/tex]So, the equation of the line with slope -1/8 that passes through the point (4,4) is
[tex]y=-\frac{1}{8}x+\frac{9}{2}[/tex]