Please, check the options of the question. The point-slope equation needs the slope, m, in the equation.
Answer:
The point-slope equation of the points (5,2) and (-1,-6) is
[tex] \\ y - 2 = \frac{4}{3}(x-5)[/tex] or,
[tex] \\ y + 6 = \frac{4}{3}(x+1)[/tex]
which are the same as
[tex] \\ 3y-4x+14 = 0[/tex] , (which is not a point-slope equation, though)
Step-by-step explanation:
The point-slope equation is given by:
[tex] \\ y - y_{1} = m(x - x_{1})[/tex]
Where m is the slope of the line:
[tex] \\ m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
Having the points (5,2) and (-1,-6), then
[tex] \\ m = \frac{-6 - 2}{-1 -5}[/tex]
[tex] \\ m = \frac{-8}{-6}[/tex]
[tex] \\ m = \frac{4}{3}[/tex]
Then, the point-slope equation of the points (5,2) and (-1,-6) is
[tex] \\ y - 2 = \frac{4}{3}(x-5)[/tex] or
[tex] \\ y + 6 = \frac{4}{3}(x+1)[/tex]
The below graph represents both lines (they are the same line).
