1. **State the problem:** Convert the linear equation $2x + 5y = 7$ into slope-intercept form. 2. **Recall the slope-intercept form:** The slope-intercept form of a line is given by: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Isolate $y$ in the given equation:** Starting with $$2x + 5y = 7$$ subtract $2x$ from both sides: $$5y = -2x + 7$$ 4. **Divide both sides by 5 to solve for $y$:** $$y = \frac{-2x}{5} + \frac{7}{5}$$ 5. **Interpret the result:** The equation in slope-intercept form is $$y = -\frac{2}{5}x + \frac{7}{5}$$ which means the slope $m = -\frac{2}{5}$ and the y-intercept $b = \frac{7}{5}$. This form is useful for graphing and understanding the behavior of the line.