Stage 8 - Q1 - 2 marks
Are \(y=3x+2\) and \(y=3x-8\) parallel?
Hint
The constant term changes position, not gradient.
Stage 8 - Q2 - 2 marks
Write a line of gradient \(-2\) through the origin.
Hint
Use \(c=0\).
Stage 8 - Q3 - 2 marks
Which pair is parallel: \(y=2x+5,\ y=5x+2,\ y=2x-1\)?
Hint
Look for matching x-coefficients.
Stage 8 - Q4 - 2 marks
Write the line parallel to \(y=4x-3\) with y-intercept 6.
Hint
Only the intercept changes.
Stage 8 - Q5 - 2 marks
Find the line parallel to \(y=-3x+7\) through \(\left(2,\ 4\right)\).
Hint
Substitute the point after choosing the required gradient.
Stage 8 - Q6 - 2 marks
Find the line parallel to \(y=2x+9\) through \(\left(4,\ 3\right)\).
Hint
Substitute the point after fixing the gradient.
Stage 8 - Q7 - 3 marks
Two lines are \(y=ax+4\) and \(y=5x-2\). Find a if they are parallel, and explain why they are not identical.
Hint
Compare both parts of \(y=mx+c\).
Stage 8 - Q8 - 3 marks
A line has the same y-intercept as \(y=3x-7\) and is parallel to \(y=-2x+4\). Find its equation.
Hint
The two conditions supply different coefficients.
Stage 8 - Q9 - 4 marks
Can two different lines be parallel and share a point? Explain using \(y=mx+c\).
Hint
What happens when the equal \(mx\) terms cancel?
Stage 8 - Q10 - 5 marks
Challenge: three parallel lines have gradient 2 and distinct positive odd integer y-intercepts. Their intercepts sum to 9, and one line passes through \(\left(3,\ 7\right)\). Find all three equations and justify uniqueness.
Hint
Use the point first, then list the remaining allowed odd pairs.