Rearrange \(2y + 6x = 10\) into the form \(y = mx + c\) and write down the gradient of the line.
Question 1 Report
Rearrange \(2y + 6x = 10\) into the form \(y = mx + c\) and write down the gradient of the line.
Answer Details
To read a gradient off an equation, it must first be arranged with \(y\) alone on the left, because only then does the number multiplying \(x\) equal the gradient.
- Subtract \(6x\) from both sides: \[ 2y = 10 - 6x \]
- Divide every term by \(2\): \[ y = 5 - 3x \] [M1]
Written in the standard order this is \(y = -3x + 5\), so
\[ \text{Gradient} = -3 \] [A1]
Two points are worth stressing. Every term must be divided by \(2\), not just the \(x\) term. And the gradient is negative, meaning the line falls as \(x\) increases; reading \(3\) from the original \(6x\) without rearranging is the usual mistake.
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