Parallel lines.?

Question

What would

y = -x
y = -x - 4

We're learning to find the distance between parallel lines. My teacher tells us to pick of the y's and she always does the top one, but it's just -x how would that work?

Answer 1

The first answer was correct up to the point at which it gave the distance between the lines.

The distance between the lines along the y axis is 4 as stated; however, that is not the perpendicular distance between the lines. In general when one asks for the distance between two lines they would mean the perpendicular distance.

It is impossible for me to be sure if your teacher is looking for the distance along the y axis or the perpendicular distance. Given the wording I would find the perpendicular distance (may be beyond your gade level). The perpendicular distance would be
4 sin (45 deg).
that is about 2.83

Note a slope of -1 implies the perpendicular line is at 45 degrees (note the sign is not important when finding the distance --> arctan (-1) = -45).

Answer 2

To find the distance between parallel lines pick a point, any point, on one of the lines and find the distance from that point to the other line.

From the first line pick the point O(0,0) and calculate the distance to the other line.

First put the equation for the second line into standard form to calculate distance. Standard form is an equation equal to zero.

y = -x - 4
x + y + 4 = 0

distance = |1*0 + 1*0 + 4| / √(1² + 1²) = 4/√2 = 2√2

Answer 3

Two lines are parallel if they have the same slope. Or, stated the other way, if two lines have the same slope then they are parallel to each other.

In your question, you have two lines.

y = -x and
y= -x -4

if you compare these two lines against the slope-intercept form equation of a line which is given as

y = mx + b

you can see that for the first line which is given as

y = -x, the slope m = -1 and intercept b = 0

While, for the second line y = -x - 4 the slope m = -1 and b = -4.

So you can see that both lines have the same slope = -1.

The first line has b=0 and is passing through the origin, while the second line has b= -4. So the distance between the two lines is = 4.

Hope this helps.