Respuesta :
Answer:
3y + 4x = 39
Explanation:
The formula for calculating the equation of a line in point-slope form is expressed as:
[tex]y-y_0=m(x-x_0)[/tex]where;
m is the slope
(x0, y0) is the point on the line
Get the slope of the required line
Given the equation of the line 3x - 4y = 8
Rewrite in standard form
-4y = -3x + 8
y = -3x/-4 + -8/4
y = 3/4 x - 2
The slope of the given line is 3/4
If the equation of the required line is perpendicular to the given line, hence the slope of the required will be:
[tex]\begin{gathered} M=\frac{-1}{(\frac{3}{4})} \\ M=\frac{-4}{3} \end{gathered}[/tex]Get the equation of the required line:
[tex]\begin{gathered} y-5=-\frac{4}{3}(x-6) \\ 3(y-5)=-4(x-6) \\ 3y-15=-4x+24 \\ 3y+4x=24+15 \\ 3y+4x=39 \end{gathered}[/tex]Hence the required equation of the line is 3y + 4x = 39
