Line Equation 487Cb1

1. **State the problem:** We need to find the equation of a line in slope-intercept form $$y=mx+b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 2. **Identify given information:** The line crosses the y-axis at $$5$$, so $$b=5$$. 3. **Find the slope $$m$$:** The line crosses the x-axis at $$-2.5$$, meaning the point $$(-2.5,0)$$ is on the line. 4. Use the slope formula $$m=\frac{y_2-y_1}{x_2-x_1}$$ with points $$(-2.5,0)$$ and $$(0,5)$$: $$m=\frac{5-0}{0-(-2.5)}=\frac{5}{2.5}$$ 5. Simplify the slope: $$m=\frac{5}{\cancel{2.5}}\times\frac{\cancel{2}}{2}=2$$ 6. **Write the equation:** Substitute $$m=2$$ and $$b=5$$ into slope-intercept form: $$y=2x+5$$ **Final answer:** $$y=2x+5$$