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
