Question: User: 3x+4y=3 the slope of a perpendicular version of this ls y=4/3+3 correct?
1. **State the problem:** We are given the line equation $$3x + 4y = 3$$ and asked if the slope of a line perpendicular to this is $$y = \frac{4}{3}x + 3$$.
2. **Find the slope of the original line:** Rewrite the equation in slope-intercept form $$y = mx + b$$.
$$3x + 4y = 3$$
Subtract $$3x$$ from both sides:
$$4y = -3x + 3$$
Divide both sides by $$4$$:
$$y = \frac{-3}{4}x + \frac{3}{4}$$
So, the slope $$m$$ of the original line is $$-\frac{3}{4}$$.
3. **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 $$-\frac{3}{4}$$ is:
$$m_{\perp} = -\frac{1}{-\frac{3}{4}} = \frac{4}{3}$$
4. **Check the given perpendicular line:** The given line is $$y = \frac{4}{3}x + 3$$.
Its slope is $$\frac{4}{3}$$, which matches the perpendicular slope we found.
**Final answer:** Yes, the slope of the perpendicular line is $$\frac{4}{3}$$, so the given line $$y = \frac{4}{3}x + 3$$ is correct.