Question

Find the gradient of the line given by 12x+4=8:
(Hint: write in Standard form First)

Answer 1

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.

1. Start with the given equation:
\[
12x + 4 = 8
\]

2. Subtract 4 from both sides to isolate the term with \( x \):
\[
12x = 8 - 4
\]
\[
12x = 4
\]

3. 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.**