Question

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)
Answer
which of the following equation would graph a line parallel to 4y=7x-x+8
Answer
plans for a stadium are drawn on a coordinate grid. One wall lies on the line y=3x+2. a perpendicular wall passes through the point (6,-8). write the equation of the line that contains the new wall.
Answer
write the equation for the vertical line that contains the point E(-12,4)
Answered by GPT 3.5
To find the equation of a line that is parallel to a given line and passes through a given point, we need to use the point-slope form of a linear equation.

The given line passes through points A(-1,2) and B(1,-6). We can find the slope of this line using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

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

Since the line we want to find is parallel to this given line, it will have the same slope.

Now, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Substituting the values:
y - 0 = -4(x - 2)

Simplifying the equation:
y = -4x + 8

Therefore, the equation of the line that passes through point W(2,0) and is parallel to the line passing through A(-1,2) and B(1,-6) is y = -4x + 8.
Answered by GPT 3.5
The given equation is 4y = 7x - x + 8. Let's simplify it first:

4y = 6x + 8
y = (6/4)x + 2
y = (3/2)x + 2

To find a line parallel to this, the slope should be the same. So any equation with a slope of (3/2) would be parallel to the given line.

Among the following options, the equation that fits this criteria is:

y = (3/2)x - 1

Therefore, the equation y = (3/2)x - 1 would graph a line that is parallel to 4y = 7x - x + 8.
Answered by GPT 3.5
To find the equation of the line for the new wall, we need to determine its slope. Since the new wall is perpendicular to the line y = 3x + 2, the slope of the new wall will be the negative reciprocal of the slope of the given line.

The slope of y = 3x + 2 is 3, so the slope of the new wall will be -1/3.

Using the point-slope form of a linear equation, we can write the equation of the line passing through the point (6, -8) and with a slope of -1/3:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point (6,-8), and m is the slope (-1/3).

Substituting the values:
y - (-8) = (-1/3)(x - 6)

Simplifying the equation:
y + 8 = (-1/3)x + 2

y = (-1/3)x - 6

Therefore, the equation of the line that contains the new perpendicular wall passing through the point (6,-8) is y = (-1/3)x - 6.
Answered by GPT 3.5
A vertical line is a line that runs straight up and down, and its equation can be written in the form x = a, where 'a' is the x-coordinate of any point on the line.

In this case, the point E has coordinates (-12, 4), so the equation for the vertical line that contains this point is:

x = -12