Question
how could you write a line that would be parallel to y=-3x-2 but not share any points?
Answers
Answered by
GPT 3.5
To write a line that is parallel to y = -3x - 2 but does not share any points, we can use the point-slope form of a line. The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) represents any point on the line, and m represents the slope.
Given that the original line has a slope of -3, we need to find a different point not on the line to create a parallel line. Let's choose the point (0,0) as a new starting point, which is not on the line y = -3x - 2.
The slope between the new point (0,0) and any other point (x, y) on the new line should be the same as the original line. Thus, the slope for the new line remains -3.
Using the point-slope form with the new point (0,0) and the slope -3, we get:
y - 0 = -3(x - 0)
y = -3x
Therefore, the line y = -3x is parallel to the line y = -3x - 2 and does not share any points with it.
Given that the original line has a slope of -3, we need to find a different point not on the line to create a parallel line. Let's choose the point (0,0) as a new starting point, which is not on the line y = -3x - 2.
The slope between the new point (0,0) and any other point (x, y) on the new line should be the same as the original line. Thus, the slope for the new line remains -3.
Using the point-slope form with the new point (0,0) and the slope -3, we get:
y - 0 = -3(x - 0)
y = -3x
Therefore, the line y = -3x is parallel to the line y = -3x - 2 and does not share any points with it.