Question

On a coordinate plane, a line passes through points (-2, -4) and (4, 2). Point P is at (0, 4). Which points lie on the line parallel to the given line?

a) (–4, 2), (–1, 3), (–2, 2)
b) (4, 2), (–5, –1), (0, 4)
c) (–1, 3), (–2, 2), (4, 2)
d) (–5, –1), (–2, 2), (0, 4)

Answer 1

To find the points on a line parallel to a given line, we need to find the slope of the given line and use it to determine the equation of the parallel line. The slope of the given line is 1. Thus, the equation of the line parallel to the given line passing through point P (0, 4) is y - 4 = x.

Step-by-step explanation:

To determine which points lie on a line parallel to the given line, we need to find the slope of the given line and use that slope to determine the equation of the parallel line.

First, we find the slope of the given line using the formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

Using the points (-2, -4) and (4, 2), we have:
Slope = (2 - (-4)) / (4 - (-2)) = 6 / 6 = 1.

So, the slope of the given line is 1. Now, to find the equation of the parallel line passing through point P (0, 4), we use the point-slope form of a line:
y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

Substituting the values, we have:
y - 4 = 1(x - 0)
y - 4 = x

This equation represents a line parallel to the given line passing through point P (0, 4).