Question

Show that the lines $$x + 2y - 5 = 0$$ and $$2x + 4y + 9 = 0$$ are parallel.

Answer 1

Rewrite each equation in the slope-intercept form $$y = mx + c$$:

For the first line:

$$x + 2y - 5 = 0$$

$$2y = -x + 5$$

$$y = -\frac{1}{2}x + \frac{5}{2}$$

Slope $$m_1 = -\frac{1}{2}$$

For the second line:

$$2x + 4y + 9 = 0$$

$$4y = -2x - 9$$

$$y = -\frac{2}{4}x - \frac{9}{4}$$

$$y = -\frac{1}{2}x - \frac{9}{4}$$

Slope $$m_2 = -\frac{1}{2}$$

Since $$m_1 = m_2 = -\frac{1}{2}$$, the two given lines have the same slope and are therefore parallel.