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
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.
To find the equation of a line parallel to a given line, you need to use the same slope.
First, let's find the slope of the line that passes through points A(-1,2) and B(1,-6). The slope formula is (y2 - y1)/(x2 - x1):
m = (-6 - 2)/(1 - (-1))
= -8/2
= -4
Since the line through point W(2,0) is parallel, it will have the same slope of -4. Now we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Substituting the values into the equation, we get:
y - 0 = -4(x - 2)
y = -4x + 8
Therefore, the equation of the line that goes through point W(2,0) and is parallel to the line through points A(-1,2) and B(1,-6) is y = -4x + 8.
The correct answer is 1. y = -4x + 8.
To find the equation of a line that is parallel to another line, we first need to find the slope of the given line. The slope of a line passing through points A(-1,2) and B(1,-6) can be calculated using the formula (y2-y1)/(x2-x1).
Let's find the slope of line AB:
m = (y2-y1)/(x2-x1) = (-6-2)/(1-(-1)) = -8/2 = -4
Since the line we want to find is parallel to line AB, it will have the same slope of -4. Now, we have the slope (m) and a point (W(2,0)) through which the line passes.
We can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values:
y - 0 = -4(x - 2)
y = -4x + 8
Therefore, the equation of the line that goes through point W(2,0) and is parallel to line AB is y = -4x + 8.
So, the correct answer is 1. y = -4x + 8.