First writing the given equation in the form y = mx + c, we get:
8y = 7x + 6 which leads to:
[tex]y= \frac{7}{8} x+\frac{3}{4}\ ................(1)[/tex]
The gradient of the line given by (1) is 7/8.
If the gradient of the perpendicular line is m we can write:
[tex]\frac{7}{8}m=-1[/tex]
Therefore m = -(8/7).
The equation of the perpendicular line is:
[tex]y=-\frac{8}{7}x+c[/tex]
Substituting the values given for the point on the perpendicular line and solving for the value of c, the required equation for the perpendicular line is:[tex]y=-\frac{8}{7}x-2\frac{6}{7}[/tex]
Writing the last equation in standard form and removing fractions, we get:
8x + 7y = -20
