Answer:
![m=3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/2y0cvxapstgefe0revyygfmq28zt6px90j.png)
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
![4x+12y=8](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ic3vm53woqk4h0yswu6e6o7wfxtio05qnp.png)
isolate the variable y
![12y=8-4x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/f9dlr2pcmypuxazyha7e2z9s5s22x4yu3m.png)
![y=(2)/(3)-(1)/(3)x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/tj8rv3cff2oo60f8mugudb79irwde0b2o4.png)
the slope of the given line is
![m=-(1)/(3)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/nkwbpt9aguxjg5oejhaujztiz42gkjmair.png)
step 2
Find the slope
of the perpendicular line to the given line
![m_1*m_2=-1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/gau1axmgaxmgs2ho1gwwcknel0gdxg03mr.png)
---> slope of the given line
![(-(1)/(3))*m_2=-1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/9vlfubaymhz6i12nl0fwcfasfw9q85zuzo.png)
![m_2=3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ranmay0n9q63uwvsq50g9icdqdddtq69mt.png)
therefore
The value of m is
![m=3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/2y0cvxapstgefe0revyygfmq28zt6px90j.png)