Question

Graph the equation. $$2 x-4 y=24$$

Short answer

The x-intercept of the graph is (12, 0) and the y-intercept is (0, -6). The line passing through these points represents the graph of the equation \(2x - 4y = 24\).

Step-by-step solution

Find the X-intercept

Set y = 0 in the equation and solve for x. So, the equation becomes \(2x - 4 \cdot 0 = 24\), which simplifies to \(2x = 24\). Solving for x results x = 12. So, the x-intercept is (12, 0).

Find the Y-intercept

Set x = 0 in the equation and solve for y. So, the equation becomes \(2 \cdot 0 - 4y = 24\), which simplifies to \(-4y = 24\). Solving for y results y = -6. So, the y-intercept is (0, -6).

Plot the points and draw the line

Plot the points (12, 0) and (0, -6) on the coordinate plane, then draw a line passing through these points. The line represents the graph of the equation \(2x - 4y = 24\).