2023HSCShort answer

Q11 (a)

2 marks

Question

The parametric equations of a line are given below.

\begin{aligned} x&=1+3t\\ y&=4t \end{aligned}

Find the Cartesian equation of this line in the form $y=mx+c$ .

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	2
Obtains $t$ in terms of $x$ , or equivalent merit	1

Sample answer:

x=1+3t

\therefore\quad t=\frac{x-1}{3}

y=4\left(\frac{x-1}{3}\right)

y=\frac{4}{3}x-\frac{4}{3}

Supplied marking guidance · human reviewed

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Syllabus alignment

Functions

Further Work with FunctionsUse algebraic and graphical representations of functions and inverse functions to model and solve problems.

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