Hint
Use the stated units and precision. Divide the signed vertical change by the horizontal change.
Worked solution
(a)
The coordinate changes give \(\displaystyle M=\)\(\displaystyle \frac{1}{2}\). Substitution of A gives \(\displaystyle c=\)\(-3\).
Answer: \(\displaystyle y=\frac{x}{2} - 3\)
(b)
Parallel lines share gradient \(\displaystyle \frac{1}{2}\). Using C determines intercept \(\displaystyle - \frac{13}{2}\).
Answer: \(\displaystyle y=\frac{x}{2} - \frac{13}{2}\)
(c)
Substitute the requested input into the complete line equation.
\(-2\) plus one gradient step is \(\displaystyle - \frac{3}{2}\).
Answer: \(\displaystyle - \frac{3}{2}\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 3 marks
- 1 mark: Calculate the gradient from both coordinate changes.
- 1 mark: Substitute a complete point to determine the intercept.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 3 marks
- 1 mark: Use equality of parallel gradients.
- 1 mark: Substitute C to determine the new intercept.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Substitute the requested input into the complete line equation.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 8 marks.