1. **State the problem:** Find the equation of the line passing through the points (0,4) and (1,6) in slope-intercept form $y=mx+b$. 2. **Formula and rules:** The slope $m$ is calculated by the formula $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1)$ and $(x_2,y_2)$ are the given points. 3. **Calculate the slope:** Using points (0,4) and (1,6), $$m=\frac{6 - 4}{1 - 0} = \frac{2}{1} = 2$$ 4. **Use slope-intercept form:** The equation is $y=2x + b$. To find $b$, substitute one point, for example (0,4), into the equation: $$4 = 2 \times 0 + b$$ 5. **Solve for $b$:** $$4 = \cancel{0} + b$$ $$b = 4$$ 6. **Final equation:** $$y = 2x + 4$$ This is the equation of the line through the points (0,4) and (1,6) in slope-intercept form.