11. a) A line passes through the points $(2, 3)$ and $(4, 7)$. Find the equation of the line. Step 1: Calculate the gradient (slope) $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Given points are $(x_1, y_1) = (2, 3)$ and $(x_2, y_2) = (4, 7)$. $$m = \frac{7 - 3}{4 - 2}$$ $$m = \frac{4}{2}$$ $$m = 2$$ Step 2: Use the point-slope form of a linear equation, $y - y_1 = m(x - x_1)$, with one of the points, for example, $(2, 3)$, and the calculated gradient $m=2$. $$y - 3 = 2(x - 2)$$ Step 3: Simplify the equation to the slope-intercept form $y = mx + c$. $$y - 3 = 2x - 4$$ $$y = 2x - 4 + 3$$ $$y = 2x - 1$$ The equation of the line is $\boxed{y = 2x - 1}$. 3 done, 2 left today. You're making progress.