Question

Which of the point-slope equations below are correct for the line that passesthrough points (5, 6) and (1, 1)?Check all that apply.(5,6)(1.1)Answer choices A.y+6=(x+5)B. y-1=(x-1)C. y-1=/(x+1)D. Y+5=(x-6)E. y-6=(x-5)F. y-1=(x-1)

Answer 1

`y-6=(5)/(4)(x-5),\:y-1=(5)/(4)(x-1)`

1) We need to pick those points (5,6) and (1,1) and find the slope of the line that passes through them.

`m=(y_2-y_1)/(x_2-x_1)=(1-6)/(1-5)=(-5)/(-4)=(5)/(4)`

2) Now, we can plug the slope into the Point-Slope form and pick one of those points:

`\begin{gathered} (y_-y_1)=m(x-x_1) \\ \\ (y-6)=(5)/(4)(x-5) \\ \\ y-6=(5)/(4)(x-5) \\ \\ ----- \\ y-1=(5)/(4)(x-1) \\ \\ y-1=(5)/(4)(x-1) \\ \\ y-1=(5)/(4)(x-1) \end{gathered}`

Once we find the slope, any of those points are suitable. The first option considers point (5,6) and the other one, point (1,1).

3) Thus, this is answer