1. **State the problem:** We are given the equation of a line in standard form: $$23x - 34y = 11$$ and need to write it in slope-intercept form $$y = mx + b$$, find the slope $$m$$, and the intercepts. 2. **Rewrite the equation in slope-intercept form:** Start with $$23x - 34y = 11$$. Subtract $$23x$$ from both sides: $$-34y = -23x + 11$$. Divide both sides by $$-34$$ to solve for $$y$$: $$y = \frac{-23x + 11}{-34} = \frac{23}{34}x - \frac{11}{34}$$. 3. **Identify the slope and y-intercept:** The slope $$m = \frac{23}{34}$$. The y-intercept $$b = -\frac{11}{34}$$. 4. **Find the x-intercept:** Set $$y=0$$ in the original equation: $$23x - 34(0) = 11 \implies 23x = 11 \implies x = \frac{11}{23}$$. 5. **Write intercepts as ordered pairs:** - x-intercept: $$\left(\frac{11}{23}, 0\right)$$ - y-intercept: $$\left(0, -\frac{11}{34}\right)$$ **Final answers:** - Equation in slope-intercept form: $$y = \frac{23}{34}x - \frac{11}{34}$$ - Slope: $$\frac{23}{34}$$ - x-intercept: $$\left(\frac{11}{23}, 0\right)$$ - y-intercept: $$\left(0, -\frac{11}{34}\right)$$