Stage 8 - Q1 - 2 marks
Classify \(y=4x-6\) by gradient sign.
Hint
Ignore the constant when deciding the slope sign.
Stage 8 - Q2 - 2 marks
Classify \(y=-3\) by gradient and intercept signs.
Hint
A constant function is horizontal.
Stage 8 - Q3 - 2 marks
Give a line with positive gradient and zero intercept.
Hint
Passing through the origin means \(c=0\).
Stage 8 - Q4 - 2 marks
A table gives \(\left(0,\ -4\right)\), \(\left(1,\ -2\right)\), \(\left(2,\ 0\right)\). Find the sign-category cell.
Hint
Read change and starting value separately.
Stage 8 - Q5 - 3 marks
Can \(y=2x+7\) and \(y=5x+1\) share the same sign-category cell although they are not parallel?
Hint
Same sign does not mean same numerical value.
Stage 8 - Q6 - 3 marks
Find one equation that is parallel to \(y=-4x+1\) and belongs to the negative-intercept column.
Hint
One condition fixes the coefficient; the other only restricts its sign.
Stage 8 - Q7 - 3 marks
A proposed grid puts \(y=6-2x\) in the positive-gradient, negative-intercept cell. Correct the placement.
Hint
The coefficient belongs to x regardless of its position in the expression.
Stage 8 - Q8 - 4 marks
Create a 3 by 3 grid using every combination of \(m=-2,\ 0,\ 2\) and \(c=-3,\ 0,\ 3\). How many distinct lines pass through the origin?
Hint
The origin condition selects an intercept, not a gradient.
Stage 8 - Q9 - 4 marks
Explain why no sign-category grid based only on gradient and intercept signs can tell whether two positive-gradient lines are parallel.
Hint
Identify the information the categories discard.
Stage 8 - Q10 - 5 marks
Challenge: choose three lines, using gradients \(-1,\ 0\) and 1 once each and intercepts \(-2,\ 0\) and 2 once each. All three must meet at one point. Find every possible set and prove there are no others.
Hint
Use the horizontal line to express the common y-value, then compare the other two equations.