Respuesta :
The given linear function is
[tex]f(x)=5x-4[/tex]This equation represents a straight line with a slope of 5. (Remember that the slope is the coefficient of the x).
Since we have to find a perpendicular line to f(x), we have to use the perpendicularity criteria to find the slope first:
[tex]m_1\cdot m_2=-1[/tex]Where the first slope is 5.
[tex]\begin{gathered} 5\cdot m_2=-1 \\ m_2=-\frac{1}{5} \end{gathered}[/tex]This means the new perpendicular line has a slope of -1/5.
Now, we use this slope, a random point (-1,2), and the point-slope formula, to find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=-\frac{1}{5}(x-(-1)) \\ y=-\frac{1}{5}(x+1)+2 \\ y=-\frac{1}{5}x-\frac{1}{5}+2 \\ y=-\frac{1}{5}x-\frac{1+10}{5} \\ y=-\frac{1}{5}x-\frac{11}{5} \end{gathered}[/tex]