Answer:
[tex]m=3[/tex]
Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
step 1
Find the slope of the given line
we have
[tex]4x+12y=8[/tex]
isolate the variable y
[tex]12y=8-4x[/tex]
[tex]y=\frac{2}{3}-\frac{1}{3}x[/tex]
the slope of the given line is
[tex]m=-\frac{1}{3}[/tex]
step 2
Find the slope [tex]m_2[/tex] of the perpendicular line to the given line
[tex]m_1*m_2=-1[/tex]
[tex]m_1=-\frac{1}{3}[/tex] ---> slope of the given line
[tex](-\frac{1}{3})*m_2=-1[/tex]
[tex]m_2=3[/tex]
therefore
The value of m is
[tex]m=3[/tex]
