1. **Problem Statement:** Find the equation of the line $y = mx + c$ for graph (a) from Question ONE. 2. **Formula and Rules:** - The slope (gradient) $m$ is calculated by the formula $$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$$ - The intercept $c$ is the value of $y$ when $x=0$, i.e., where the line crosses the y-axis. 3. **Given Points for Graph (a):** $(0,1)$ and $(1,2)$. 4. **Calculate the slope $m$:** $$m = \frac{2 - 1}{1 - 0} = \frac{1}{1} = 1$$ 5. **Find the intercept $c$:** Since the line passes through $(0,1)$, the y-intercept is $c = 1$. 6. **Write the equation of the line:** $$y = 1x + 1$$ 7. **Final answer:** The equation of the line for graph (a) is $$\boxed{y = x + 1}$$