Question: Select the equation that is equivalent to $3x - 4y = 8$.
y = -4/3x + 8/3
y = -3/4x + 2
y = 3/4x - 2
y = 4/3x - 8/3
1. **State the problem:** We need to find which equation is equivalent to the given linear equation $$3x - 4y = 8$$.
2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept.
3. **Isolate $$y$$:** Starting with $$3x - 4y = 8$$,
$$-4y = -3x + 8$$
4. **Divide both sides by $$-4$$:**
$$y = \frac{-3x + 8}{-4}$$
Use cancellation notation:
$$y = \frac{\cancel{-3}x + \cancel{8}}{\cancel{-4}} = \frac{3}{4}x - 2$$
5. **Final equivalent equation:**
$$y = \frac{3}{4}x - 2$$
6. **Compare with the options:** The equivalent equation matches the option:
$$y = \frac{3}{4}x - 2$$
**Answer:** $$y = \frac{3}{4}x - 2$$