Question

What is the equation in point -slope form of a line that passes through the points (7,-8) and (-4,6)? A. y-6=-2/3(x+4) B. y+6=-14/11(x-4) C. y+6=-2/3(x-4) D. y-6=-14/11(x+4)

Answer 1

Given two points  (x₁,y₁) and (x₂,y₂)the slope passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)

In this case the slope will be:
(7,-8)
(-4,6)
m=(6+8)/(-4-7)=14/-11=-14/11

point-slope form of a line: we need a point (x₀,y₀) and the slope (m).
y-y₀=m(x-x₀)

In this case, we know the slope (m=-14/11), and we can choose either of two points. The line will be the same.

(-4,6)
m=-14/11
y-y₀=m(x-x₀)
y-6=-14/11(x+4)        ⇒ (point-slope form)

Answer:  D.  y-6=-14/11(x+4)