What is an equation of the line that passes through the points ( 6 , 5 ) (6,5) and ( 3 , 5 ) (3,5)?

Answer 1

For given points, first start by finding the slope between them The formula for slope is:

m =y₂ - y₁/x₂ - x₁

m = 5-5/3-6

m = 0/-3 = 0

With 0 slope, the line is perfectly horizontal. The equation is found like this:

y - y₁ = m(x - x₁)

y - 5 = 0(x - 6)

y - 5 = 0

y = 5

Answer 2

Since the y-value for each point is the same, 5, the line is horizontal. Therefor the equation of the line is y = 5.

To really prove this you can look at the slope m = Δy/Δx and the point-slope formula y - y₁ = m(x - x₁) to really prove it to yourself.

For the slope of (6, 5) and (3,5) we calculate this by finding the difference in y-values divided by the difference in x-values.

Δy = 5 - 5 = 0

Δx = 3 - 6 = -3

m = 0/-3 = 0, so the slop is zero. Using the formula y - y₁ = m(x - x₁) you can pick either point you like, let's use the (6, 5) point so

y - 5 = 0(x - 6)

y - 5 = 0

y = 5

It checks out.