Question

Find the equation of the straight line passing through the point (3,5)

which is perpendicular to the line
y = 3x + 2

Answer 1

y = -
`(1)/(3)` x + 6

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 2 ← is in slope- intercept form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(3)`, thus

y = -
`(1)/(3)` x + c ← is the partial equation

To find c substitute (3, 5) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

y = -
`(1)/(3)` x + 6 ← equation of perpendicular line

Answer 2

x -3y -18=0

Explanation:

To find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y = 3x + 2, we will first find the slope(m).

To find the slope m of the perpendicular equation;

y = 3x + 2 --------------(1)

comparing the equation above with the standard equation of a circle

y=mx + c

m=3

The slope of perpendicular equation;

`m_(1)m_(2)` = -1

3
`m_(2)` = -1

Divide both-side of the equation by 3

`m_(2)` = -1/3

so, the slope of our perpendicular equation is -1/3

Then, we go ahead to find our intercept

To find the intercept, we will plug in the points and the new slope into the formula y =mx + c

5 = -
`(1)/(3)`(3) + c

5 = -1 +c

Add one to both-side of the equation

5+1 = -1 + c + 1

6 =c

c=6

our intercept c is equal to 6

so we can now proceed to form our equation.

y = -
`(1)/(3)` x + 6

Multiply through by 3

-3y = -x + 18

We can rearrange the equation, hence;

x -3y -18=0

Therefore the equation of the straight line that passes through the point (3,5) which is perpendicular to the line y = 3x + 2 is x -3y -18=0