What is the relationship between two lines whose slopes are −7 and 1/7?

a) The lines are parallel to each other
b) The lines are mirror images of each other, reflected over the x-axis
c) The lines always cross at the origin.
d) The lines are mirror images of each other, reflected over the y-axis.
e) The lines are perpendicular to each other.

the lines are perpendicular to each other

To determine the relationship between two lines given their slopes, we can use the fact that parallel lines have equal slopes, and perpendicular lines have slopes that are negative reciprocals of each other.

The slopes given are -7 and 1/7.

Since the slopes are not equal, we can eliminate options a) and c).

To determine if the lines are mirror images of each other, we need to compare the signs of the slopes.

The slope -7 is negative, and the slope 1/7 is positive.

If lines are mirror images of each other, reflected over the x-axis, their slopes must have opposite signs. Therefore, we can eliminate option b).

Similarly, if lines are mirror images of each other, reflected over the y-axis, their slopes must be equal in magnitude but have opposite signs. This means that we can eliminate option d) as well.

The only option left is e) The lines are perpendicular to each other since their slopes are negative reciprocals of each other. Hence, the correct answer is e) The lines are perpendicular to each other.

To determine the relationship between two lines based on their slopes, you can use the following rules:

1. If the slopes are equal, the lines are parallel.
2. If the slopes are negative reciprocals of each other (i.e., multiplying one slope by -1 gives you the other), the lines are perpendicular.
3. If the slopes have different values but are not equal and not negative reciprocals of each other, the lines will intersect at some point.

In this case, the given slopes are -7 and 1/7.

Since the slopes are not equal and not negative reciprocals of each other, option a) and option e) can be eliminated.

Now, let's compare the slopes:

-7 ≠ 1/7

Since the slopes are not equal, the lines are not parallel. Therefore, option a) is incorrect.

If the lines were perpendicular, the second slope would be the negative reciprocal of the first slope. Let's check:

-7 ≠ -1/7

Since the slopes are not negative reciprocals of each other either, the lines are not perpendicular. Therefore, option e) is also incorrect.

Finally, the only possibility left is that the lines intersect at some point. This means they have a common solution, and that solution represents their point of intersection.

Therefore, the correct answer is c) The lines always cross at the origin.

I am going to graph

y = -7x and y = (1/7)x for you

www.wolframalpha.com/input/?i=plot+y+%3D+-7x+%2B1,+y+%3D+(1%2F7)x+%2B1+from+-10+to+10

let you decide how they are related.
Notice Wolfram used a different scale for the y-axis than the x-axis,
making y = (1/7)x look like it falls on the x-axis. It doesn't !

suggestion: plot a few points for each one, draw the straight line on a 1:1 scale grid.