Perpendicular gradient and intercept

Practise perpendicular gradient and intercept with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

A line L has equation $3x+2y=12$. A line N passes through $(2,1)$ and is perpendicular to L. (a) Find the gradient of L. [1 marks] (b) Find the equation and x-intercept of N. [3 marks]

Worked explanation

• Part (a)

  Rearrange to $y=-3x/2+6$, so the gradient is $-3/2$.

• Part (b)

  The perpendicular gradient is $2/3$. Thus $y-1=\frac23(x-2)$, giving $y=2x/3-1/3$. Set $y=0$ to obtain $x=1/2$.

(a) $-3/2$.; (b) $y=2x/3-1/3$; $(1/2,0)$.

Original VectorPaths practice; not an official VCAA question or marking rubric.