Question

Line passing through $(1,2)$ and $(2,5)$ is:

• A. $3x-y+1=0$
• B. $3x+y+1=0$
• C. $y-3x+1=0$
• D. $3x+y-1=0$

Answer 1

The correct option is C

$y-3x+1=0$

Explanation for the correct answer:

Finding the equation of the line passing through the two points:

Given points are $(1,2)$ and $(2,5)$.

Finding the slope using the formula, $m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the values we get,

$$\begin{gathered} m=\frac{5-2}{2-1} \\ m=3 \end{gathered}$$

Equation of the line is given by,

$$\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-2=3(x-1) \\ \Rightarrow 3x-y-1=0 \\ \Rightarrow y-3x+1=0 \end{gathered}$$

Hence, option (C) is the correct answer.