Question

how do u write the equation of the line that passes through the points (3,-5) and (1,-9). I have to put it in fully reduced point-slope form unless it's a vertical or horizontal line

Answer 1

We have to calculate the equation of the line in slope-point form:

`y-y_1=m(x-x_1)`

The information we have is two points: (3,-5) and (1,-9).

First, we use one point to fill the spaces for (x1,y1). We pick (3,-5), but any of both will do.

Then we have:

`y+5=m(x-3)`

We will replace x and y with the coordinates of the second point (1,-9) in order to calculate the slope:

`\begin{gathered} (-9)+5=m(1-3) \\ -4=m\cdot(-2) \\ m=(-4)/(-2) \\ m=2 \end{gathered}`

Then, the equation becomes:

`y+5=2(x-3)`