If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: 8th grade (Illustrative Mathematics)>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?

• I cannot take it anymore
• fr I already know this! why do I have to watch this!?!?!??! my teacher is silly
(1 vote)
• 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.
• 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.
• 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?
• 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).
• What's linear?
• linear lines means straight lines
• who invented/discovered linear equations and why?
• Sir William Rowan Hamilton, an Irish mathematician, invented linear equations in the year 1843. He induced relationships between various variables to find their values. To date, we use linear equations to solve numerous mathematical problems. The general representation of a linear equation is given by: ax + by = c.
• Are there any possibility that a linear equation can't convert into slope intercept form?
• Good question!

In the coordinate plane, the only type of line with an equation that can't be converted into y = mx + b form (slope-intercept form) is a line with an equation equivalent to the form x = c, where c is a constant.

This exceptional type of line is a vertical line with undefined slope. The graph has no y-intercepts if c is nonzero, and all real numbers for its y-intercepts if c is zero.

Have a blessed, wonderful day!