Question

(-4,-1) that is perpendicular to the line with the equation 4x+5y=5 how do I do this

Answer 1

To find the line that is perpendicular to the one we have, the first step is to rewrite the expression in the slope-intercept form.

$\begin{gathered} 4x+5y=5 \\ 5y=5-4x \\ y=\frac{5-4x}{5} \\ y=-\frac{4}{5}x+1 \end{gathered}$

The slope of this line is -4/5. The one that is perpendicular to it has a slope that is negative reciprocal to this one, which means that we need to invert the fraction and the signal.

$\begin{gathered} m=-(\frac{1}{\frac{-4}{5}}) \\ m=-(\frac{-5}{4})_{} \\ m=\frac{5}{4} \end{gathered}$

The equation for the perpendicular line so far is:

$y=\frac{5}{4}x+b$

To find "b" we need to replace the coordinates of (-4,-1) and solve for b.

$\begin{gathered} -1=\frac{5}{4}\cdot(-4)+b \\ -1=-5+b \\ b=-1+5 \\ b=4 \end{gathered}$

The full expression is:

$y=\frac{5}{4}x+4$