1. **Problem 1: Find the equation of a straight line** Given two points on a line, $A(2,3)$ and $B(5,11)$, find the equation of the line passing through these points. 2. **Problem 2: Determine the gradient and intercept** For the line with equation $y = 4x - 7$, find the gradient and the y-intercept. 3. **Problem 3: Graph interpretation** A line passes through points $C(0,2)$ and $D(3,8)$. Draw the graph and find the equation of the line. 4. **Problem 4: Parallel and perpendicular lines** Find the equation of a line parallel to $y = 2x + 5$ passing through the point $(1,4)$. 5. **Problem 5: Real-life application** A taxi company charges a fixed fee of 3 plus 2 per kilometer. Write the equation for the total cost $C$ in terms of kilometers $k$ and find the cost for 10 kilometers. --- **Solutions:** 1. Gradient $m = \frac{11-3}{5-2} = \frac{8}{3}$. Equation: $y - 3 = \frac{8}{3}(x - 2)$, simplified to $y = \frac{8}{3}x - \frac{7}{3}$. 2. Gradient is 4, y-intercept is $-7$. 3. Gradient $m = \frac{8-2}{3-0} = 2$. Equation: $y - 2 = 2(x - 0)$ or $y = 2x + 2$. 4. Parallel line has same gradient $m=2$. Equation: $y - 4 = 2(x - 1)$ or $y = 2x + 2$. 5. Equation: $C = 3 + 2k$. For $k=10$, $C = 3 + 2 \times 10 = 23$. **Answers:** 1. $y = \frac{8}{3}x - \frac{7}{3}$ 2. Gradient = 4, y-intercept = $-7$ 3. $y = 2x + 2$ 4. $y = 2x + 2$ 5. $C = 3 + 2k$, $C(10) = 23$