What is the equations of a line that goes through point W(2,0) and is parallel to a line that goes though A)-1,2) and B(1,-6)?

1. y=-4x+8
2. y=4x+2
3. y=-4x+2
4. y=4x-8

1 answer

To find the equation of a line parallel to the line passing through points A(-1,2) and B(1,-6), we first need to find the slope of the original line.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)

Using the coordinates A(-1,2) and B(1,-6):
m = (-6 - 2) / (1 - (-1))
m = -8 / 2
m = -4

Since the line we are looking for is parallel to the original line, it will have the same slope of -4.

Now we can use the point-slope form of a linear equation to find the equation of the line passing through point W(2,0):
y - y₁ = m(x - x₁)

Plugging in the values, m = -4, x₁ = 2, and y₁ = 0:
y - 0 = -4(x - 2)
y = -4x + 8

Therefore, the correct equation for the line passing through point W(2,0) and parallel to the line passing through points A(-1,2) and B(1,-6) is:
y = -4x + 8

So, the correct answer is 1. y = -4x + 8.