Intersection of two linear models

Practise intersection of two linear models with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Two lines have equations $y=2x+1$ and $y=-x+10$. (a) Find their point of intersection. [2 marks] (b) Find the area of the triangle formed with the y-axis. [2 marks]

Worked explanation

• Part (a)

  Equate the right sides: $2x+1=-x+10$, giving $3x=9$, $x=3$, and then $y=7$.

• Part (b)

  The y-intercepts are $(0,1)$ and $(0,10)$, giving base $9$. The perpendicular height is the x-coordinate $3$, so area $=\frac12(9)(3)=27/2$.

(a) $(3,7)$.; (b) $27/2$ square units.

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