Given parameters:
Equation of the line given 2x - 7y = 13
Coordinates of points = -3, 8
Unknown:
Equation of a line perpendicular = ?
Solution;
To find the equation of this line, simply find the negative inverse of the given line.
m = [tex]-\frac{1}{m}[/tex]
2x - 7y = 13 , this is an equation of a straight line
let us write it in the form y = mx + c so as to derive the slope
y and x are coordinates
m is the slope
c is the y intercept
2x - 7y = 13;
-7y = -2x + 13
divide through by -7;
y = [tex]\frac{2}{7}x[/tex] + [tex]\frac{13}{7}[/tex]
The slope of this line is [tex]\frac{2}{7}[/tex];
Now the slope of a line perpendicular to it will be [tex]-\frac{7}{2}[/tex];
the equation of the line will be;
y = [tex]-\frac{7}{2} x + C[/tex]
Since the coordinate of this line is (-3,8) , let us find C;
y = 8 and x = -3;
8 = [tex]-\frac{7}{2}[/tex] (-3) + C
multiply through by 2;
16 = 21 + 2C
16 - 21 = 2C
-5 = 2C
C = [tex]\frac{-5}{2}[/tex]
Now the equation of the line is;
y = [tex]-\frac{7}{2} x + \frac{5}{2}[/tex]
