Answer:
The point slope equation be [tex]y = \frac{1x}{2}-5[/tex] .
Step-by-step explanation:
The point slope equation of the line is given by .
[tex](y-y_{1})=m (x-x_{1})[/tex]
Where m is the slope .
[tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m =\frac{1-(-3){12-4}[/tex]
[tex]m =\frac{4}{8}[/tex]
[tex]m = \frac{1}{2}[/tex]
As given
The point-slope form of the equation of the line that passes through (4, -3) and (12, 1) is [tex]\frac{1}{2}[/tex] .
Putting the values in the point slope equation .
[tex](y-(-3))=\frac{1}{2}(x-4)[/tex]
[tex]2\times (y+3)=x-4[/tex]
2y + 6 = x - 4
2y = x - 4 - 6
2y = x -10
[tex]y = \frac{1x}{2}-\frac{10}{2}[/tex]
[tex]y = \frac{1x}{2}-5[/tex]
Therefore the point slope equation be [tex]y = \frac{1x}{2}-5[/tex] .
