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### Unit 3: Lesson 7

Lesson 11: Equations of all kinds of lines

# Converting to slope-intercept form

Learn to convert equations like 4x + 2y = -8 into slope-intercept form. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• On line A why did he divide all terms by 2?
• In order to eliminate the coefficient (2) on Y. If the coefficient were left attached to that Y right there, then we would not have a value for Y by itself, which is what the slope-intercept equation requires.
• why did he subtract 4? shouldnt he divide by 4?
• Why would he divide? the addition sign is next to it so he has to do the opposite
• Could anybody please tell me how you graph a fractional number, like y=5/8x+8/9
• Koorosh,
y=5/8x+8/9 is a linear equation. So you just want to find any two points. plot the two points, and draw a line through the two point you plotted.
If you choose 0 for x then y=5/8 * 0 + 8/9 = 8/9 so your first point is (0,8/9)
If you choose 8 for x then y = 5/8 * 8 + 8/9 = 5 + 8/9 = 5 8/9
so another point is (8,5 8/9).
So plot the point (0,8/9) which is just below of (0,1) and
plot the point (8, 5 8/9) which is just below of (5,6)
and then draw a line through the two points.

The other method you can use is to plot the y-intercept.
The equation y=5/8x+8/9 is is slope y-intercept form
so the y intercept is at (0,8/9). Plot that point.
The slope is 5/8, so from your y-intercept point, count right 8 and then go up 5. And remember it is just below the line as you count going up.

The graph should look something like this: https://www.khanacademy.org/cs/y58x-89/5900563254345728

I hope that helps make it click for you.
• At time you said that you can't make it into slope interval form. Then you made a line at -2x. Why where you able to do that. Also what is the x mean in "y=mx+b".
• when your m is -2 why did you go over one and down two?
• In y=mx+b must b be a whole number
• No, b does not have to be a whole number. b is simply where the line will cross the y-axis when this line is graphed. So, if b=1/2 then the line will cross the y axis between the 0 and the 1.
• What's linear?
• linear lines means straight lines
• How did he get (0,-4) from y= -2x- 4?
• To find the y intercept, set x=0. This gives y = -2(0)-4=-4. Thus, y intercept is (0,-4).
• At how did Sal instantly know the slope of the line?

Also, if y= mx +b, shouldn't the slope in y = -2x - 4 be -2? the slope is m, and in the first equation is being multiplied by the x, so without the x the slope in the second equation would be -2?
• how do i find the slope intercept form if the equation is written differently?
• You would convert it by isolating the Y variable
• Are there any possibility that a linear equation can't convert into slope intercept form?