ANSWER
[tex]y=-3x+10[/tex]
EXPLANATION
The general form of the equation of a line is:
[tex]y=mx+b[/tex]
where m = slope
b = y-intercept
A line that is perpendicular to another line has a slope that is the negative inverse of the slope of the line.
Hence, the slope of the line we are looking for is:
[tex]\begin{gathered} -\frac{1}{\frac{1}{3}} \\ \Rightarrow-3 \end{gathered}[/tex]
Now, we can apply the point-slope method to find the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]
where (x1, y1) = point that the line passes through
Therefore, the equation of the line is:
[tex]\begin{gathered} y-4=-3(x-2) \\ y-4=-3x+6 \\ y=-3x+6+4 \\ y=-3x+10 \end{gathered}[/tex]
That is the answer.
