Question

Which line set of points are part of a line that is parallel to the line y = (-23)x + 1

A (3,-2), (6,0)
B. (2,-2), (6,4)
C. (2,0), (2, -1)
D. (5,0), (-1,4)

Answer 1

The line set of points that is part of a line parallel to the given line is option D, (5,0) and (-1,4).

Step-by-step explanation:

The line equation is given as y = -23x + 1. Parallel lines have the same slope, so we need to find the slope of this line. The slope is the coefficient of x in the equation. So the slope of the given line is -23.

Now, let's check each line set of points to see if they have the same slope:

1. For option A, the slope is -2/3, so it is not parallel to the given line.
2. For option B, the slope is 6/4 = 3/2, which is not parallel to the given line.
3. For option C, the slope is (0-(-1))/2-2) = 1/0, which is not defined. It means the line is vertical and cannot be parallel to the given line.
4. For option D, the slope is (4-0)/(-1-5) = -4/6 = -2/3, which is the same as the given line. So, option D is parallel to the given line.

Therefore, the line set of points that is part of a line parallel to the given line is option D, (5,0) and (-1,4).