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# Parallel lines from equation (example 3)

Sal determines which pairs out of a few given linear equations are parallel. Created by Sal Khan and Monterey Institute for Technology and Education.

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• When two lines have the same slope, but they also have the same y-intercept (they lie on each other), are they considered parallel?
• Excellent question,
If two lines had the same slope and same y-intercept, they would not be considered parallel lines.

They would be considered as coincident lines--lines that lie directly on top of each other.
• At for the slope formula of y=6 i thought the slope is 6 and the y intercept is 0? Is that right? If not, why isn't it?
• If the slope was 6, there would be a x after the 6.
• (5, -5), parallel to y = - 3\5 x + 2
• Using y=mx+b
if it is parallel, means it has the same slope.
So your slope m = -3/5
the coordinate (x,y) is (5,-5)
Now you can substitute them into y=mx+b and solve for b.
• at why do you divde them all by 2??
• Line A equation is given as 2y = 12x + 10
We use slope of the line to find out if lines are parallel. Slope is read easily from the slope-intercept form, which looks like this:
y = ax + b (where a is the slope)
So how can we easily turn 2y = 12x + 10 into something that starts with "y = "?

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We divide both sides of the equation by 2 :)
• Are lines that are negative reciprocals perpendicular?
• Yes, but you will probably often see different wording. The way you might hear it is that perpendicular lines have opposite reciprocal slopes. You should have the word slope somewhere in your question. The idea is that if it is positive, the perpendicular line would have a negative slope, but if the line has a negative slope, then the perpendicular would have a positive slope. If the slope of a line is -3, then the perpendicular line has a slope of 1/3.
• hello. i don't know how to solve this problem. i have to find the equation:
intersects with y=2x-1 on the y-axis and is parallel to y=-x
Thank you!
• y = 2x - 1 implies that the y-intercept for the equation you are looking for is -1.

y = -x implies that the slope of the equation you are looking for is -1.

Plugging in these two pieces of information into the slope intercept form (y = mx + b) results in:

y = -x - 1
• What if for Line B x=6 what would we need to do then?
• If I have 2 slopes for example 150\120 and my second slope 125/100 are they opposite reciprocal slope?
• How would I write an equation with parallel lines? An example is: write an equation through (9,-1) and parallel yo y=-5x+7.
• Your given line y = -5x +7, is in slope intercept form, so you can see the slope is -5.
Use the point slope form to quickly write an equation. Because the line you want is parallel, you know it has the same slope as your given line.
So the parallel line will also have slope -5. It goes thru (9.-1);
Point slope form is y - y1 = m (x - x1); here y1 = -1 and x1= 9 and m=-5
y - -1 = -5(x -9)
y+1 = -5(x-9)
With a little algebra you can change this to slope intercept form if you need that.