Line rule from two points

Practise line rule from two points with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

A straight line passes through $A(-2,5)$ and $B(4,-4)$. (a) Find its gradient and equation. [2 marks] (b) Find the x-intercept exactly. [1 marks]

Worked explanation

• Part (a)

  $m=(-4-5)/(4+2)=-3/2$. Using A, $y-5=-\frac32(x+2)$, so $y=-3x/2+2$.

• Part (b)

  Set $y=0$: $3x/2=2$, hence $x=4/3$.

(a) $m=-3/2$, $y=-3x/2+2$.; (b) $(4/3,0)$.

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