Question

What is the equation of the line with y-intercept of 6 and is perpendicular to the line y=−3x+2 ?

Answer 1

Answer :

y = x/3 + 6

Note :

★ Slope y-intercept form of straight line :

y = mx + c , where m is the slope and c is the y-intercept of the line .

★ If two lines having the slopes m and m' are perpendicular , then m•m' = -1 .

Solution :

Here ,

The given equation is ;

y = -3x + 2

Comparing the given equation with slope y-intercept form of line y = mx + c ,

We have ,

slope , m = -3

y-intercept ,c = 2

Now ,

Form the required line ,

slope = m' (say)

y-intercept , c' = 6 (given)

Since ,

The given line and required line are perpendicular thus ,

=> m•m' = -1

=> m' = -1/m

=> m' = -1/-3

=> m' = 1/3

Thus ,

The required equation of line will be given as ;

=> y = m'x + c'

=> y = (1/3)x + 6

=> y = x/3 + 6 (slope y-intercept form)

OR

=> y = (x + 18)/6

=> 6y = x + 18

=> x - 6y + 18 = 0 (general form)

Hence ,

Required equation is : y = x/3 + 6