Question

Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.(4, 1), (2,3)

Answer 1

It is given that the line passes through points (x1, y1)=(4, 1) and (x2, y2)=(2, 3).

The two point form of the equation of a line is given by,

`y-y1=(y2-y1)/(x2-x1)(x-x1)`

Substitute the known values in the above equation.

`\begin{gathered} y-1=(3-1)/(2-4)(x-4) \\ y-1=(2)/(-2)(x-4) \\ y-1=-1(x-4) \\ y-1=-x+4 \\ y=-x+4+1 \\ y=-x+5 \end{gathered}`

Therefore, the equation of the line is y=-x+5.