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

1 answer

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.