The general equation of a line is given by:
[tex]\begin{gathered} y=mx+c \\ \text{where m = slope} \\ c=\text{intercept} \end{gathered}[/tex]Given the line 2x -4y = -3
Step 1: Re-write the equation by making y the subject
[tex]\begin{gathered} 4y=2x+3 \\ y=\frac{2}{4}x+\frac{3}{4} \\ y=\frac{1}{2}x+\frac{3}{4} \end{gathered}[/tex]Since we have the equation of the line to be
[tex]y=\frac{1}{2}x+\frac{3}{4}[/tex]Step 2: Obtain the slope of this line
[tex]\text{slope}=m=\frac{1}{2}[/tex]Step 3: Obtain the slope perpendicular to this line.
If two line are perpendicular, then
[tex]m_1m_2=-1[/tex]so that
[tex]m_2=-\frac{1}{m_1}[/tex][tex]m_2=-\frac{1}{\frac{1}{2}}=-2[/tex]Hence the slope of the new line will be = -2
Step 4: Obtain the equation of the line using the formula:
[tex]y-y_1=m(x-x_1)[/tex]where
[tex]\begin{gathered} x_1=3,y_1=4,and\text{ } \\ m=-2 \end{gathered}[/tex]Thus,
[tex]y-4=-2(x-3)[/tex]=>
[tex]\begin{gathered} y-4=-2x+6 \\ y=-2x+6+4 \\ y=-2x+10 \end{gathered}[/tex]The equation of the line that s perpendicular to the line is
=> y= -2x +10
This can also be written in the form ax+by=c
as
Making the constant to be on the right-hand side and the variables to be on the left and side as shown below
Hence,
2x+y=10
