Find the equation of the line that passes through the points (2,5) and (-1,-4). Write the equation in the form ax+by+c=0.

easy 2 marks Class 10 · Mathematics · Coordinate Geometry

Answer

3 x - y - 1 = 0

The correct answer is $3 x - y - 1 = 0$ — Thus the required equation is $3 x - y - 1 = 0$ .

Step-by-step solution

Compute the slope using $m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}$ .
Substitute $y_{2} = - 4$ , $y_{1} = 5$ , $x_{2} = - 1$ , $x_{1} = 2$ to get $m = \frac{- 4 - 5}{- 1 - 2} = \frac{- 9}{- 3} = 3$ .
Use the point‑slope form $y - y_{1} = m (x - x_{1})$ with point (2,5): $y - 5 = 3 (x - 2)$ .
Expand: $y - 5 = 3 x - 6 \Rightarrow 3 x - y - 1 = 0$ .
Thus the required equation is $3 x - y - 1 = 0$ .

Common mistake: Mixing up the order of subtraction in the slope formula leading to a sign error.

Concept tested: Equation of line through two points