Option [tex]y-5 = -\frac{6}{5} (x-6)[/tex] is the point-slope form for the given point.
Step-by-step explanation:
Step 1:
As we have the slope, m and a coordinate we can use the point-slope form to find the equation.
m = [tex]-\frac{6}{5}[/tex] and the coordinate is (6, 5) assume this to be ([tex]x_{1}, y_{1}[/tex]).
The point-slope form is [tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex].
Step 2:
For the given point, [tex]x_{1} = 6[/tex] and [tex]y_{1} = 5[/tex] and m = [tex]-\frac{6}{5}[/tex].
Substituting these values in the equation, we get
[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex] becomes [tex]\left(y-5\right)=-\frac{6}{5} \left(x-6\right)[/tex].
This is the first option that is given.
