1) Use the point on the line and the slope m of the line to find three additional points through which the line passes. (There are many correct answers.)
(3, −2), m = 0
a) (3, −2), (3, −4), (3, −6)
b) (3, 4), (3, 1), (3, 11)
c) (6, −2), (6, −4), (6, 2)
d) (0, −4), (−1, −4), (−2, −4)
e) (7, −2), (−4, −2), (0, −2)
since m=0, all the points have y = -2
trick question.
To find three additional points through which the line passes, we can use the given information - a point on the line (3, -2) and the slope m = 0.
The slope of a line is given by the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.
In this case, since the slope is 0, it means that the line is horizontal. A horizontal line has the same y-coordinate for all points on the line.
So, we need to find three points that have the same y-coordinate as the given point (3, -2).
Comparing the options:
a) (3, -2), (3, -4), (3, -6) - all points have the same x-coordinate but different y-coordinates.
b) (3, 4), (3, 1), (3, 11) - all points have the same x-coordinate but different y-coordinates.
c) (6, -2), (6, -4), (6, 2) - all points have the same x-coordinate but different y-coordinates.
d) (0, -4), (-1, -4), (-2, -4) - all points have different x-coordinates but the same y-coordinate.
e) (7, -2), (-4, -2), (0, -2) - all points have different x-coordinates but the same y-coordinate.
From the given options, option d) (0, -4), (-1, -4), (-2, -4) satisfies the criteria. All three points have the same y-coordinate (-4) as the given point (3, -2).
So, the correct answer is d) (0, -4), (-1, -4), (-2, -4).