Equations of a straight line: Secrets of the Mathematical Ninja

"$y$," said the student, carelessly, "$=mx+c$," and before he knew it, his wrists and ankles were secured to the table and a laser was slowly, but extremely surely, cutting the table in two.

The Mathematical Ninja continued the lesson. "I think you mean $y - y_1 = m(x-x_1)$," he said, patiently.

"Er... yes," said the student. "Obviously."

"So, we know the gradient..."

"Four-fifths!" said the student, eagerly.

The Mathematical Ninja smiled; he would have sped the laser up if the student had said 0.8. "And a point..."


"Very good, so we can..."

"Substitute those in! $y - 3 = \frac45(x-6)$."

"And then what?"

The student said "You expect me to multiply a fraction into a bracket while strapped to a table with a laser between my legs?"

The Mathematical Ninja said "No, I expect you to die." He paused for a second. "Sorry, no. I expect you to cross-multiply. My bad."

"Oh!" said the student. "So I can multiply the 5 onto the other side to get $5y-15 = 4x - 24$?"


"Or... $4x - 5y - 9 = 0$?"


"And can I get off this thing now?"

Pout. "I suppose."

The laser stopped, and the Mathematical Ninja wondered where he was going to get a new table from.


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

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