Question

Find the equation of the given line.Find the equation of the line passing through (1, 6) and (3,5).y =

Answer 1

The given points are (1,6) and (3,5).

First, we find the slope using the formula below.

`m=(y_2-y_1)/(x_2-x_1)`

Replacing the points, we have.

`m=(5-6)/(3-1)=(-1)/(2)=-(1)/(2)`

Now, we use the point-slope formula, the slope, and one point.

`\begin{gathered} y-y_1=m(x-x_1) \\ y-6=-(1)/(2)(x-1) \\ y-6=-(1)/(2)x+(1)/(2) \\ y=-(1)/(2)x+(1)/(2)+6 \\ y=-(1)/(2)x+(1+12)/(2) \\ y=-(1)/(2)x+(13)/(2) \end{gathered}`

Therefore, the equation of the line is

`y=-(1)/(2)x+(13)/(2)`