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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

Sagot :

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

[tex]y-y_1=m(x-x_1)[/tex]

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:

[tex]y+5=m(x-3)[/tex]

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

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

Then, the equation becomes:

[tex]y+5=2(x-3)[/tex]

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