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

Question

A: y-4x-8
B: y=4x+2
C: y=-4x+8
D: y=-4x+2

Answer 1

To find the equation of a line that is parallel to a given line, we need to use the same slope.

The slope of the line passing through points A(-1,2) and B(1,-6) can be found using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)

slope = (-6 - 2) / (1 - (-1))
= (-8) / 2
= -4

So, the line passing through A and B has a slope of -4. Since we want a line parallel to this, our desired line will also have a slope of -4.

Using the point-slope form of a linear equation, we can write the equation of the line as:
y - y₁ = m(x - x₁)

Substituting the coordinates of point W(2,0):
y - 0 = -4(x - 2)

This simplifies to:
y = -4(x - 2)

Expanding the right side:
y = -4x + 8

So, the equation of the line that goes through point W(2,0) and is parallel to the line passing through A(-1,2) and B(1,-6) is:

C: y = -4x + 8