Question
Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).
4x − y = −6
x + 4y = 7
x − 4y = −9
4x + y = 2
4x − y = −6
x + 4y = 7
x − 4y = −9
4x + y = 2
Answers
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Answered by
GPT 3.5
To find the equation of a line passing through two points, we first need to find the slope of the line. The formula for calculating the slope given two points is:
slope = (y₂ - y₁) / (x₂ - x₁)
Given the points (-1, 2) and (3, 1), the slope is:
slope = (1 - 2) / (3 - (-1))
slope = -1 / 4
Next, we can use the point-slope form of the equation of a line to find the equation:
y - y₁ = m(x - x₁)
Using the point (-1, 2) as the base point:
y - 2 = (-1/4)(x - (-1))
y - 2 = (-1/4)(x + 1)
y - 2 = (-1/4)x - 1/4
y = (-1/4)x + 2 - 1/4
y = (-1/4)x + 7/4
So, the equation that represents a line passing through the points (-1, 2) and (3, 1) is:
y = (-1/4)x + 7/4
Therefore, the correct option is not listed in the given choices.
slope = (y₂ - y₁) / (x₂ - x₁)
Given the points (-1, 2) and (3, 1), the slope is:
slope = (1 - 2) / (3 - (-1))
slope = -1 / 4
Next, we can use the point-slope form of the equation of a line to find the equation:
y - y₁ = m(x - x₁)
Using the point (-1, 2) as the base point:
y - 2 = (-1/4)(x - (-1))
y - 2 = (-1/4)(x + 1)
y - 2 = (-1/4)x - 1/4
y = (-1/4)x + 2 - 1/4
y = (-1/4)x + 7/4
So, the equation that represents a line passing through the points (-1, 2) and (3, 1) is:
y = (-1/4)x + 7/4
Therefore, the correct option is not listed in the given choices.
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