Question

Are these lines parallel perpendicular or neither -2x + 5y = 15 5x + 2y = 12

Answer 1

If we have the equation of the from

$y=mx+b$

Then a line perpendicular to that equation is

$y=-\frac{1}{m}x+c$

Let us bring each of the lines in slope-intercept form.

$\begin{gathered} -2x+5y=15 \\ 5y=15+2x \\ y=\frac{2}{5}x+3 \end{gathered}$

The other equation in slope-intercept form is

$\begin{gathered} 5x+2y=12 \\ 2y=12-5x \\ y=-\frac{5}{2}x+6 \end{gathered}$

As we can see the second equation is negative of the reciprocal of the second equation; therefore, the two lines are perpendicular.

$y(x)\text{ = }\frac{\text{2}}{5}x+3\text{ y(x) =-}\frac{5}{2}x+6$$m_1=\frac{2}{5}_{}\rightarrow m_2=\frac{-5}{2}$