Which of the following is the equation of the line passing through the points (2,3) and (5,11)?

easy MCQ 2 marks Class 9 · Mathematics · Coordinate Geometry

Answer

y = \frac{8}{3} x - \frac{7}{3}

The correct answer is A) $y = \frac{8}{3} x - \frac{7}{3}$ — Step 4: Match the simplified equation with the options. Option A matches exactly.

Step-by-step solution

Step 1: Find the slope $m$ using $m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}} = \frac{11 - 3}{5 - 2} = \frac{8}{3}$ because the slope of a line is the change in $y$ divided by the change in $x$ .
Step 2: Use the point‑slope form $y - y_{1} = m (x - x_{1})$ with point $(2, 3)$ . This gives $y - 3 = \frac{8}{3} (x - 2)$ .
Step 3: Simplify to slope‑intercept form: $y = \frac{8}{3} x - \frac{16}{3} + 3 = \frac{8}{3} x - \frac{7}{3}$ .
Step 4: Match the simplified equation with the options. Option A matches exactly.

Common mistake: Using the wrong pair of points or miscomputing the slope

Concept tested: Equation of a straight line through two points