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=(5-4x)/(5) \\ y=-(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=-((1)/((-4)/(5))) \\ m=-((-5)/(4))_{} \\ m=(5)/(4) \end{gathered}`

The equation for the perpendicular line so far is:

`y=(5)/(4)x+b`

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

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

The full expression is:

`y=(5)/(4)x+4`