Question

write equation of the line containing (2,6) and (3,1)

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)=(2,6)$ and $(x_2,y_2)=(3,1)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{1 - 6}{3 - 2}=\frac{-5}{1}=- 5$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(2,6)$ and $m=-5$, we have $y - 6=-5(x - 2)$.

Step3: Simplify to slope - intercept form

Expand the right side: $y - 6=-5x + 10$. Then add 6 to both sides to get $y=-5x+16$.

Answer:

There is no correct option among the given ones. The correct equation of the line is $y=-5x + 16$.