Respuesta :
If two lines with slopes m₁ and m₂ are perpendicular, then:
[tex]m_1\times m_2=-1[/tex]Isolate y to write the given line in slope-intercept form. Identify the slope of the line as the coefficient of x and find the slope of a line perpendicular to it using the given relationship between the slopes of perpendicular lines.
Starting from the equation:
[tex]-3x-9y=-4[/tex]Isolate y:
[tex]\begin{gathered} \Rightarrow3x+9y=4 \\ \Rightarrow9y=4-3x \\ \Rightarrow y=\frac{4}{9}-\frac{3}{9}x \\ \\ \therefore y=-\frac{1}{3}x+\frac{4}{9} \end{gathered}[/tex]Then, the slope of the given line is -1/3. Let m be the slope of a line perpendicular to -3x-9y=-4. Then:
[tex]\begin{gathered} (-\frac{1}{3})\times m=-1 \\ \Rightarrow m=\frac{-1}{(-\frac{1}{3})}=3 \\ \\ \therefore m=3 \end{gathered}[/tex]Therefore, the slope of a line perpendicular to the given line is 3.
Two parallel lines have the same slope.
Therefore, the slope of a line parallel to the given line is -1/3.
