Question

Which of the following lines does not intersect

A.
y=-3x-7
B.
y = 3x + 7
y=-3x+7?
C. y = 3x - 7
1
D.
y = 3x

Answer 1

Answer: B. y = 3x + 7 and y = -3x + 7 are parallel lines, so they do not intersect.

Explanation:

Two lines in a plane may intersect at a point, be parallel, or be coincident (overlapping). To determine which of the given lines do not intersect, we need to find the slope of each line and check for parallelism.

The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Therefore, we can write the equations of the given lines in slope-intercept form as follows:

A. y = -3x - 7 (slope m = -3)

B. y = 3x + 7 (slope m = 3)

C. y = 3x - 7 (slope m = 3)

D. y = 3x (slope m = 3)

From the slopes, we can see that lines B and C have the same slope of 3, so they are parallel. Therefore, they do not intersect at any point in the plane. Lines A and D have different slopes, so they are not parallel and will intersect at some point in the plane.

Answer 2

D

Explanation:

The line in option D, y = 3x, does not intersect with any of the other lines.

To see this, we can first note that options A and B have slopes of -3 and 3, respectively, which means they are parallel lines. Therefore, they will never intersect.

Option C has a slope of 3 as well, but its y-intercept is -7, which is different from the y-intercept of line B, which is 7. This means that these two lines are not parallel and will intersect at some point.

On the other hand, line D has a slope of 3 and a y-intercept of 0 (since there is no constant term), which means it passes through the origin. Therefore, it will not intersect with any of the other lines unless one of the other lines also passes through the origin, which is not the case here.

Therefore, the line that does not intersect with any of the other lines is option D, y = 3x.