Write down the gradient of the line \(y=8-3x\).
Question 1 Report
Write down the gradient of the line \(y=8-3x\).
Answer Details
The gradient of a straight line is the coefficient of \( x \) once the equation is arranged in the form \( y = mx + c \), where \( m \) is the gradient and \( c \) is the \( y \)-intercept.
The equation \( y = 8 - 3x \) can be rewritten by swapping the order of the terms on the right:
\[ y = -3x + 8 \]Comparing with \( y = mx + c \) gives \( m = -3 \), so the gradient is \( -3 \) [B1].
The trap is the way the equation is written: the number 8 comes first, which tempts the answer 8, and the minus sign is easy to drop, giving 3. The sign carries real meaning. A negative gradient means the line slopes downwards from left to right, so for every 1 unit increase in \( x \) the value of \( y \) falls by 3. The intercept, \( c = 8 \), is the separate piece of information that the line crosses the \( y \)-axis at \( (0,\,8) \).
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