Question

Write the equation of the line that goes through the point
(2,6) and is perpendicular to the line –3x - y = 8.

Answer 1

Answer:

The equation is y = (1/3)x + 16/3 or 3y = x + 16 .

Step-by-step explanation:

You have to rearrange the equation in the form of y = mx + b :

$- 3x - y = 8$

$y = - 3x - 8$

When both lines are perpendicular to each other, their gradient multiplied together will form -1 :

$m1 \times m2 = - 1$

$let \: m1 = - 3$

$let \: m2 = perpendicular \: line$

$- 3 \times m2 = - 1$

$m2 = - 1 \div - 3$

$m2 = \frac{1}{3}$

So the equation of perpendicular line is y = (1/3)x + b. Next, you have to find the value of b by substituting (2,6) into the equation :

$y = \frac{1}{3} x + b$

$let \: x = 2,y = 6$

$6 = \frac{1}{3} (2) + b$

$6 = \frac{2}{3} + b$

$b = 6 - \frac{2}{3}$

$b = \frac{16}{3}$