Question

Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).

a 4x − y = −6
b x + 4y = 7
c x − 4y = −9
d 4x + y = 2

Answer 1

To find the equation of the line passing through two points, we can first find the slope of the line using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Where (x₁, y₁) = (-1, 2) and (x₂, y₂) = (3, 1)

m = (1 - 2) / (3 - (-1))
m = -1 / 4
m = -1/4

Now that we have the slope, we can use the point-slope formula to find the equation of the line:

y - y₁ = m(x - x₁)

Using the first point (-1, 2):

y - 2 = (-1/4)(x - (-1))
y - 2 = (-1/4)(x + 1)
y - 2 = (-1/4)x - 1/4
y = (-1/4)x - 1/4 + 2
y = (-1/4)x + 7/4

Therefore, the equation that represents a line passing through points (-1, 2) and (3, 1) is:

y = (-1/4)x + 7/4

So none of the given equation options are correct.