Question

Determine the equation of the straight line whose gradient is  and which intersects the y-axis at a distance of 4 units from the origin.

sol?​

Answer 1

Step-by-step explanation:

Line AB intersects the y-axis 2 units above origin.

As we know that at y-axis, abscissa (x-coordinate) will be 0 always.

∴ Line AB cuts y-axis at P(0,2)

Also line AB makes an angle of 30° with the x-axis.

∴ Slope of the line =tan30°=

3

1

As we know that equation of a line passing through (x

0

,y

0

) and having slope m is-

(y−y

0

)=m(x−x

0

)

Therefore equation of the line AB is-

(y−2)=

3

1

(x−0)

⇒x−

3

y+2=0

Hence the required answer is x−

3

y+2=0