Question

The equation of the line that is perpendicular to the line 5x + 6y = 18 and passes through the point (10,7)

Answer 1

y = ( 6 / 5 )x - 5;

Step-by-step explanation:

Perpendicular Line Theory

y = - ( 1 / m )x + c;

Algebra

Convert dual intercept to standard form.

5x + 6y = 18;

Subtract 5x from both sides.

6y = - 5x + 18;

Divide both sides by 6.

y = ( - 5x + 18 ) / 6;

y = ( - 5x / 6 ) + ( 18 / 6 );

y = ( - 5 / 6 )x + 3;

Get the perpendicular line.

y = ( 6 / 5 )x + c;

Substitute the point.

7 = ( 6 / 5 )( 10 ) + c;

7 = 12 + c;

Subtract 12 from both sides.

- 5 = c;

c = - 5;

y = ( 6 / 5 )x - 5;