Question
Passes through the points (5,1) and (-1,4)
Answers
GPT 3.5
We can use the formula for the equation of a line given two points (x₁, y₁) and (x₂, y₂):
(y - y₁) = ((y₂ - y₁) / (x₂ - x₁)) * (x - x₁)
Using the given points (5,1) and (-1,4), we substitute the values into the formula:
(y - 1) = ((4 - 1) / (-1 - 5)) * (x - 5)
Simplifying,
(y - 1) = (-3/(-6)) * (x - 5)
(y - 1) = (1/2) * (x - 5)
Multiply both sides by 2 to get rid of the fraction:
2(y - 1) = x - 5
Distributing,
2y - 2 = x - 5
Rearranging the equation to the standard form,
x - 2y = -3
Therefore, the equation of the line that passes through the points (5,1) and (-1,4) is x - 2y = -3.
(y - y₁) = ((y₂ - y₁) / (x₂ - x₁)) * (x - x₁)
Using the given points (5,1) and (-1,4), we substitute the values into the formula:
(y - 1) = ((4 - 1) / (-1 - 5)) * (x - 5)
Simplifying,
(y - 1) = (-3/(-6)) * (x - 5)
(y - 1) = (1/2) * (x - 5)
Multiply both sides by 2 to get rid of the fraction:
2(y - 1) = x - 5
Distributing,
2y - 2 = x - 5
Rearranging the equation to the standard form,
x - 2y = -3
Therefore, the equation of the line that passes through the points (5,1) and (-1,4) is x - 2y = -3.