Respuesta :
Parallel lines have the same slopes
The product of the slopes of the perpendicular lines is -1, which means if the slope of one line m, then the slope of the perpendicular line is -1/m (reciprocal it and change its sign)
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope
Then to find the slope of a line from its equation put the equation in the form above
Since the given equation is
[tex]-5x-6y=-7[/tex]Add 5x to both sides
[tex]\begin{gathered} -5x+5x-6y=-7+5x \\ -6y=-7+5x \\ -6y=5x-7 \end{gathered}[/tex]Now, divide both sides by -6 to make the coefficient of y = 1
[tex]\begin{gathered} \frac{-6y}{-6}=\frac{5x}{-6}-\frac{7}{-6} \\ y=-\frac{5}{6}x+\frac{7}{6} \end{gathered}[/tex]By comparing it by the form of the equation above to find m
[tex]m=-\frac{5}{6}[/tex]The slope of the given line is -5/6
a) The slope of the parallel line is the same as the slope of the given line
[tex]m_1=m_2=-\frac{5}{6}[/tex]b) to find the slope of the perpendicular line flip the fraction and change its sign
[tex]\begin{gathered} m_1=-\frac{5}{6} \\ m_2=\frac{6}{5} \\ m_1\times m_2=-\frac{5}{6}\times\frac{6}{5}=-1 \end{gathered}[/tex]The slope of the perpendicular line is 6/5
