1. **State the problem:** Solve the linear equation for $y$ and understand its graph. 2. **Given equation:** $$-2y + 5x = 2$$ 3. **Goal:** Express $y$ in terms of $x$ to find the slope-intercept form $y = mx + b$. 4. **Isolate $y$:** $$-2y = 2 - 5x$$ 5. **Divide both sides by $-2$:** $$y = \frac{2 - 5x}{-2}$$ 6. **Use cancellation to simplify:** $$y = \frac{\cancel{2} - 5x}{\cancel{-2}} = -\frac{2}{2} + \frac{5x}{2} = -1 + \frac{5}{2}x$$ 7. **Rewrite in slope-intercept form:** $$y = \frac{5}{2}x - 1$$ 8. **Interpretation:** The slope is $\frac{5}{2}$ and the y-intercept is $-1$. 9. **Check points:** For $x = -4$, $$y = \frac{5}{2}(-4) - 1 = -10 - 1 = -11$$ For $x = 6$, $$y = \frac{5}{2}(6) - 1 = 15 - 1 = 14$$ (Note: The points given in the graph description do not lie exactly on this line, so the graph might be approximate or from a different equation.) **Final answer:** $$y = \frac{5}{2}x - 1$$