What is an equation of the line that passes through the points ( 5 , − 1 ) and ( − 5 , 1 )

Question

What is an equation of the line that passes through the points (5,−1) and (−5,1)

Answer 1

To find the equation of the line, first find the slope.

To find the slope, use the slope equation:

where "m" is the slope, (x₁, y₁) is the first point, and (x₂, y₂) is the second point. Since the points are (5, -1) and (-5, 1) then x₁ = 5, y₁ = -1, x₂ = -5, and y₂ = 1. Plug those in to get:

m = (1 - -1)/(-5 - 5) = (1 + 1)/(-10) = 2/-10 = -1/5

Then use the point-slope form of a line which is: y - y₁ = m(x - x₁) where "m" is the slope you calculated above and (x1, y1) is one of the two points above. It can be either point. Let's pick (5. -1) so x₁ = 5 and y₁ = -1. Plug those in to get:

y - -1 = (-1/5)(x - 5)

y + 1 = (-1/5)x + 1

y = (-1/5)x