Question: What is the slope of a line perpendicular to $2x-4y=7$
1. **State the problem:** We need to find the slope of a line perpendicular to the line given by the equation $$2x - 4y = 7$$.
2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$, where $$m$$ is the slope.
Starting with $$2x - 4y = 7$$:
$$-4y = -2x + 7$$
Divide both sides by $$-4$$:
$$y = \frac{-2x + 7}{-4}$$
Simplify the fraction:
$$y = \frac{-2x}{-4} + \frac{7}{-4} = \frac{1}{2}x - \frac{7}{4}$$
3. **Identify the slope of the original line:** From the equation $$y = \frac{1}{2}x - \frac{7}{4}$$, the slope $$m = \frac{1}{2}$$.
4. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal of the original slope.
The negative reciprocal of $$\frac{1}{2}$$ is $$-\frac{1}{\frac{1}{2}} = -2$$.
**Final answer:** The slope of the line perpendicular to $$2x - 4y = 7$$ is $$-2$$.