Recall that two lines are perpendicular if the product of their slopes is equal to -1.
Notice that f(x) is given in slope-intercept form, then, the slope of f(x) is 3. Therefore, the slope of g(x) must be
[tex]-\frac{1}{3}\text{.}[/tex]
Now, to determine the equation of g(x) we will use the following formula:
[tex]y(x)-y_0=m(x-x_0),[/tex]
where (x₀,y₀) is a point on the line, and m is the slope.
Substituting m=-1/3 and (x₀,y₀)=(3,1), we get:
[tex]g(x)-1=-\frac{1}{3}(x-3)\text{.}[/tex]
Taking the above equation to its slope-intercept form we get:
[tex]g(x)=-\frac{1}{3}x+2.[/tex]
Answer:
Slope:
[tex]-\frac{1}{3}=-0.33\text{.}[/tex]
Equation:
[tex]\begin{gathered} g(x)=-\frac{1}{3}x+2. \\ g(x)=-0.33x+2. \end{gathered}[/tex]
