5 mistakes learners make with parallel and perpendicular lines, each one named and explained.
Parallel lines share a gradient; perpendicular gradients multiply to give minus one.
y = -3x + 1 is chosen as parallel to y = 3x + 1, because the constants match.
The two equations look strikingly similar, and the matching number is the visible one.
Question. Parallel to y = 3x + 1
A common answer. y = -3x + 1
The answer. y = 3x - 5
Why. Matching the constant only means they cross the y-axis at the same point, which makes them meet.
Parallel is entirely about the gradient. The constant is what makes them different lines.
The reciprocal of the gradient is chosen when a parallel line was asked for.
Parallel and perpendicular are learned together and both are about the gradient.
Question. Parallel to y = 5x + 2
A common answer. y = (1/5)x + 2
The answer. y = 5x - 3
Why. A parallel line has the identical gradient, with no change at all.
Parallel is the easy one. If you had to calculate anything, you were doing the other.
The perpendicular gradient of 2 is given as 1/2.
Turning the fraction upside down is the visible half of the rule.
Question. Perpendicular to y = 2x + 1
A common answer. 1/2
The answer. -1/2
Why. 2 times 1/2 is 1, and perpendicular gradients have to multiply to -1.
Multiply your two gradients together. Only -1 confirms a right angle.
The gradient is copied unchanged when a perpendicular one was asked for.
Same gradient is the rule that is remembered, and only the word in the question differs.
Question. Perpendicular to y = 2x + 1
A common answer. gradient 2
The answer. gradient -1/2
Why. Two lines with the same gradient are parallel and never meet at a right angle.
Multiply the two gradients. Perpendicular ones always give -1.
The perpendicular gradient of 2 is given as -2.
Changing the sign is the other visible half of the rule, taken on its own.
Question. Perpendicular to y = 2x + 1
A common answer. -2
The answer. -1/2
Why. 2 times -2 is -4, not -1.
The rule has two halves. Flip it and change the sign, both.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.