To find the gradient (or slope) of the line given by the equation \( 12x + 4 = 8 \), we will first rearrange the equation into a form that we can easily identify the slope.
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Start with the given equation: \[ 12x + 4 = 8 \]
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Subtract 4 from both sides to isolate the term with \( x \): \[ 12x = 8 - 4 \] \[ 12x = 4 \]
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Now, divide both sides by 12 to solve for \( x \): \[ x = \frac{4}{12} \] \[ x = \frac{1}{3} \]
This equation \( x = \frac{1}{3} \) represents a vertical line.
For a vertical line, the slope (gradient) is undefined because there is no change in \( y \) as \( x \) changes. Vertical lines do not have a defined slope, hence the gradient is:
Undefined.