How could you write the equation of a line that would be parallel to y=−3x−2 but not share any points?(1 point) Responses y=3x−2 y equals 3 x minus 2 y=3x+8 y equals 3 x plus 8 y=−3x+8 y equals negative 3 x plus 8 y=−3x−2
The equation of a line that is parallel to y = -3x - 2 but does not share any points can be given as:
y = -3x + c, where c ≠ -2
How could you write the equation of a line that would be parallel to y=−3x−2 but not share any points?(1 point) Responses y=3x−2 y +3 x -2 y=3x+8 y = 3 x + 8 y=−3x+8 y = - 3 x plus 8 y=−3x−2
To find the equation of a line that is parallel to y = -3x - 2 and does not share any points, we need to consider that parallel lines have the same slope.
The given line has a slope of -3, so the parallel line will also have a slope of -3.
Knowing the slope (-3) and the fact that the line should not share any points with y = -3x - 2, we can choose any arbitrary point and write the equation using the point-slope form of a line equation.
Let's use the point (0, 0).
Now we can write the equation of the line using the point-slope form:
y - y1 = m(x - x1)
y - 0 = -3(x - 0)
y = -3x
Therefore, the equation of a line that is parallel to y = -3x - 2 and does not share any points is y = -3x.
To find an equation of a line that is parallel to y = -3x - 2 but does not share any points, you need to follow the slope-intercept form of a linear equation, which is y = mx + b, where "m" is the slope and "b" is the y-intercept.
The given equation y = -3x - 2 already provides the slope, which is -3. Parallel lines have the same slope. Let's use this information to find a different y-intercept.
To create a line that does not intersect the original line, you can choose any value for the y-intercept as long as it is not -2 (the y-intercept of the original line). Let's choose a different y-intercept, such as 8.
So, the equation of a line parallel to y = -3x - 2 but not sharing any points would be y = -3x + 8.
Note: You could choose different values for the y-intercept, as long as it is not -2, and still have a line parallel to the given line.