Stage 8 - Q1 - 2 marks
State the gradient and y-intercept.
Hint
Read the coefficient and constant in \(y=mx+c\).
Stage 8 - Q2 - 2 marks
State the gradient and y-intercept.
Hint
Include the negative sign with the coefficient.
Stage 8 - Q3 - 2 marks
State the gradient and y-intercept.
Hint
A horizontal line has no rise.
Stage 8 - Q4 - 2 marks
A line rises by 9 while x rises by 3. Find its gradient.
Hint
The gradient is a ratio, not just the vertical change.
Stage 8 - Q5 - 2 marks
Find the gradient through \(\left(-1,\ 5\right)\) and \(\left(3,\ -3\right)\).
Hint
Both coordinate differences need the same direction.
Stage 8 - Q6 - 2 marks
A line has gradient 3 and passes through \(\left(2,\ 11\right)\). Find its equation.
Hint
The point determines the constant once the gradient is known.
Stage 8 - Q7 - 3 marks
A graph uses 2 units per horizontal grid square and 5 per vertical square. A line rises 3 squares across 5 squares. Find its gradient.
Hint
Count coordinate units, not just squares.
Stage 8 - Q8 - 3 marks
The line \(y=2x-7\) meets the x-axis. Find that point and explain why \(-7\) is not its x-intercept.
Hint
Use the correct zero coordinate.
Stage 8 - Q9 - 4 marks
A line passes through \(\left(-2,\ 7\right)\) and \(\left(4,\ -5\right)\). Find its equation and the x-value when \(y=-9\).
Hint
Use differences rather than the final coordinate alone.
Stage 8 - Q10 - 5 marks
Challenge: a line has gradient \(\frac{-3}{2}\) and contains points \(\left(a,\ 9\right)\) and \(\left(a+8,\ -3\right)\), where a is unknown. Does this information determine a unique line? Give two valid examples or prove uniqueness.
Hint
The difference in x is known, but is either absolute x-coordinate known?