Q. \(2x – 4y = -12\).

Solution

1. Write the given linear equation.

   \(2x – 4y = -12\)

2. Isolate the term that contains y by removing the 2x term from the left side. Do this by subtracting 2x from both sides of the equation. This keeps the equality balanced because the same operation is performed on both sides.

   \(2x – 4y – 2x = -12 – 2x\)

   Simplify the left and right sides.

   \(-4y = -2x – 12\)

3. Now solve for y by dividing every term by -4. Dividing by -4 isolates y because -4 is the coefficient of y.

   \(\dfrac{-4y}{-4} = \dfrac{-2x – 12}{-4}\)

   Simplify the left side to y and simplify the right side by distributing the division over the sum.

   \(y = \dfrac{-2x}{-4} + \dfrac{-12}{-4}\)

   Each fraction simplifies: \(\dfrac{-2x}{-4} = \dfrac{1}{2}x\) and \(\dfrac{-12}{-4} = 3\).

   Therefore

   \(y = \dfrac{1}{2}x + 3\)

4. Interpret the result (slope-intercept form). The equation is now in the form y = mx + b, where m is the slope and b is the y-intercept.

   Slope: \(m = \dfrac{1}{2}\)

   Y-intercept: \(b = 3\), which corresponds to the point \((0,\,3)\).

5. Find the x-intercept by setting y = 0 and solving for x.

   Start from the original equation or use the solved form; using the original is straightforward:

   \(2x – 4(0) = -12\)

   \(2x = -12\)

   \(x = \dfrac{-12}{2} = -6\)

   X-intercept: \((-6,\,0)\).

Final solved form: \(y = \dfrac{1}{2}x + 3\). The slope is \(\dfrac{1}{2}\), the y-intercept is \((0,\,3)\), and the x-intercept is \((-6,\,0)\).