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# Parallel lines from equation

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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• I need help with finding the equation of a line parallel to another line. Say the first line has a slope of 2/5 and passes through (3, -5). How would I get the equation of a line parallel to that? My math book ain't helpin'.
• First, use the point-slope form to convert the details you were given into a slope-intercept equation. Then, change the y-intercept to get a line parallel to the original. Finally, stop referring to a textbook and invest in learning at Khan Academy.
(1 vote)
• How to prove lines parallel
• You have to find the slopes of the two lines, if they are the same, then the lines are parallel unless they are the exact same line.
• What do you do if it tells you y=x? Like for example;
y=x
x+Y=-2?
• If you subtract x on both sides, you will get y=-x+2. This shows that the slopes are opposite reciprocals (1/1 and -1/1) and thus lines are perpendicular. If you just have a variable, the coefficient is an invisible 1 (or in slope terms 1/1).
• at around Sal says you increase by one. I didn't see that in the equation anywhere, how did he get that?
• He just picked a random number to increase by. He could have increased by 1,2,3,4,5.....
He would just have to make sure that whatever number he did pick, he would multiply it by two to know how much to go up.
Does that make sense? Please tell me if it doesn't!
• does it matter if one of the slopes is negative and the other is positive? are they still parallel or not?
• Parallel lines will always have the same slope, so there cannot be one positive and one negative, these lines will always intersect somewhere. Perpendicular lines almost always have opposite signs, so they could possibly be perpendicular.
• Hello! I have a quick question...

How come you can't simplify a fraction in an equation?

My assignment was to write an equation of a line that is perpendicular to
y = 7/5x + 6, that passes through point (2,-6).

My answer was y = -5/7x - 4 4/7

It said that I was incorrect however, so I looked at the hints.
The hints said the answer was y = -5/7x - 32/7
This is the same answer just not simplified.
Is there a reason you cannot simplify the fractions in the equation?
• Usually the question will ask you not to use mixed numbers. Another way to look at 4 & 4/7 is ((4 * 7 + 4) / 7) Where as "unsimplified" is (32 / 7). So when you simplify it to the mixed number form, you are actually making it less simplified by adding extra steps if you were to solve the equation.
• what if you have y=3x+4 and it passes through (-2,3)
• I'm assuming you want a line parallel to y = 3x + 4. All this means is that the slope will be 3 and the y intercept will not be 4. or in otherwords y = mx+b, m = 3 and b doesn't equal 4

Now, as long as you have a slope and point you can find the equation of the line. And you do, you want a slope of 3 and a point (-2,3). To use this you use point slope form. y - y1 = m(x - x1) where (x1, y1) is the point you want. and m is slope. So just fill in and solve.

y - y1 = m(x - x1) with m = 3 and (x1, y1) = (-2,3)
y - 3 = 3(x - -2)

If you prefer KC's way just start with y = 3x + b then b = y - 3x where you plug in (-2, 3) for x and y, or in other words:

b = y - 3x where x = -2 and y = 3. Then again just plug in and solve. then plug b into y = 3x + b

You get the same answer either way.
• I have a question, please answer it. Y = -4/3x + 6. Is this Perpendicular?
(1 vote)
• perpendicular to what other line? Two lines are perpendicular if they have opposite reciprocal slopes, so any line with a slope of 3/4 would be perpendicular to this line such as y = 3/4 x
• i dont understand the concept at
(1 vote)
• Slope intercept form is:
change in y
------------
change in x

slope intercept form tells us how much y_ changes for every _x

Line A has a slope of 2, so basically that means for every 2 that y_ changes by, _x changes by 1