Question

Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.(2, -3), (4,5)

Answer 1

It is given that the line passes through points (x1, y1)=(2, -3) and (x2, y2)=(4, 5).

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 to obtain the equation of the line.

`\begin{gathered} y-(-3)=(5-(-3))/(4-2)(x-2) \\ y+3=(8)/(2)(x-2) \\ y+3=4(x-2) \\ y+3=4x+4*(-2) \\ y+3=4x-8 \\ y=4x-8-3 \\ y=4x-11 \end{gathered}`

Therefore, the equation of the line is y=4x-11.