i don't really get it why in the last exercise the slope is -3/2 you ad plus 2 for the change in x but minus 3 for the change in y.

Because -3/2 is basically equal to minus 3 by PLUS 2

How come if the negative sign is next to the fraction it causes the rise to be negative but not the run

Think about the fraction as division... How do you get a negative number when dividing: a negative divided by a positive = a negative a positive divided by a negative = a positive As you can see, only one of the 2 numbers can be negative. Thus, for a slope like -4/5, you can apply the negative sign to the numerator which would tell you to go down 4 units, then right 5 units. Or, you can apply the negative to the denominator which would make you go up 4 units and left 5 units. If you make both numbers negative, then you are doing: negative divided by negative = positive. And, you would have a positive slope. Hope this helps.

How do I graph a line if the slope isn't provided? Here is what I mean: y=-x+6 How do I graph it if I do not know the slope? Thanks!

When a variable doesn't have a variable, it's safe to assume the variable is 1. So, -x would be -1x or -1/1x. Hope that makes sense!

I don't have a clue on how to do this

If you have an equation in slope-intercept form, you know both a point (the y intercept) and the slope, so it should be relatively easy to graph especially with a little practice. So if you have y=3x-4, the slope is 3=3/1, the y intercept is (0,-4). We can plot the point by starting at the origin and counting down 4 to get to (0,-4) and put a dot at this point. With a slope of rise (up) 3 over run (right) 1, you get to (0+1,-4+3) which is (1,-1), and a second time (1+1,-1+3) which is (2,2) and you have three points to draw a line through. One more example, if you have y=-3/4x + 2, you have a point (0,2) and a slope of -3/4 (rise down 3 right 4). This gives a second point of (0+4,2-3) or (4,-1) and (4+4,-1-3) or (8,-4) to draw a line. So start with the y intercept, and count the slope from that point.

what if the question is y=x+4

Remember, "x" is the same as "1x". So, the slope of the equation is 1 and the y-intercept is (0,4). Hope this helps.

I can't understand how to graph an equation with a fraction y-intercept. Ex: y=2x-1/2

Put a point at (0, -1/2). It is half-way between 0 and -1. Since the slope is 2, you move up 2 units and right 1. -- Up 1 unit takes you to 1/2, up 2 units takes you to 1 1/2 (halfway between 1 and 2). -- Then, go right 1 unit. You should now be at the point 1 1/2, 1) Hope this helps.

Main content

Algebra basics

Course: Algebra basics > Unit 4

Lesson 6: Slope-intercept form intro

Graphing slope-intercept form

Google Classroom

Learn how to graph lines whose equations are given in the slope-intercept form y=mx+b.

If you haven't read it yet, you might want to start with our introduction to slope-intercept form.

Graphing lines with integer slopes

Let's graph y, equals, 2, x, plus, 3.

Recall that in the general slope-intercept equation y, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #0d923f, b, end color #0d923f, the slope is given by start color #ed5fa6, m, end color #ed5fa6 and the y-intercept is given by start color #0d923f, b, end color #0d923f. Therefore, the slope of y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, plus, start color #0d923f, 3, end color #0d923f is start color #ed5fa6, 2, end color #ed5fa6 and the y-intercept is left parenthesis, 0, comma, start color #0d923f, 3, end color #0d923f, right parenthesis.

In order to graph a line, we need two points on that line. We already know that left parenthesis, 0, comma, start color #0d923f, 3, end color #0d923f, right parenthesis is on the line.

Additionally, because the slope of the line is start color #ed5fa6, 2, end color #ed5fa6, we know that the point left parenthesis, 0, start color #ed5fa6, plus, 1, end color #ed5fa6, comma, start color #0d923f, 3, end color #0d923f, start color #ed5fa6, plus, 2, end color #ed5fa6, right parenthesis, equals, left parenthesis, 1, comma, 5, right parenthesis is also on the line.

[How do we know that?]

Check your understanding

Problem 1

Graph y, equals, 3, x, minus, 1.

Problem 2

Graph y, equals, minus, 4, x, plus, 5.

Graphing lines with fractional slope

Let's graph y, equals, start color #ed5fa6, start fraction, 2, divided by, 3, end fraction, end color #ed5fa6, x, start color #0d923f, plus, 1, end color #0d923f.

As before, we can tell that the line passes through the y-intercept left parenthesis, 0, comma, start color #0d923f, 1, end color #0d923f, right parenthesis, and through an additional point left parenthesis, 0, start color #ed5fa6, plus, 1, end color #ed5fa6, comma, start color #0d923f, 1, end color #0d923f, start color #ed5fa6, plus, start fraction, 2, divided by, 3, end fraction, end color #ed5fa6, right parenthesis, equals, left parenthesis, 1, comma, 1, start fraction, 2, divided by, 3, end fraction, right parenthesis.

While it is true that the point left parenthesis, 1, comma, 1, start fraction, 2, divided by, 3, end fraction, right parenthesis is on the line, we can't plot points with fractional coordinates as precisely as we draw points with integer coordinates.

We need a way to find another point on the line whose coordinates are integers. To do that, we use the fact that in a slope of start color #ed5fa6, start fraction, 2, divided by, 3, end fraction, end color #ed5fa6, increasing x by start color #ed5fa6, 3, end color #ed5fa6 units will cause y to increase by start color #ed5fa6, 2, end color #ed5fa6 units.

[Why is that so?]

This gives us the additional point left parenthesis, 0, start color #ed5fa6, plus, 3, end color #ed5fa6, comma, start color #0d923f, 1, end color #0d923f, start color #ed5fa6, plus, 2, end color #ed5fa6, right parenthesis, equals, left parenthesis, 3, comma, 3, right parenthesis.

Check your understanding

Problem 3

Graph y, equals, start fraction, 3, divided by, 4, end fraction, x, plus, 2.

Problem 4

Graph y, equals, minus, start fraction, 3, divided by, 2, end fraction, x, plus, 3.

Want to join the conversation?

Sort by:

682060
Posted 5 years ago. Direct link to 682060's post “How come if the negative ...”
How come if the negative sign is next to the fraction it causes the rise to be negative but not the run
Button navigates to signup pageComment on 682060's post “How come if the negative ...”
(24 votes)
Answer
- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “Think about the fraction ...”
  Think about the fraction as division... How do you get a negative number when dividing:
  a negative divided by a positive = a negative
  a positive divided by a negative = a positive
  
  As you can see, only one of the 2 numbers can be negative. Thus, for a slope like -4/5, you can apply the negative sign to the numerator which would tell you to go down 4 units, then right 5 units. Or, you can apply the negative to the denominator which would make you go up 4 units and left 5 units.
  
  If you make both numbers negative, then you are doing: negative divided by negative = positive. And, you would have a positive slope.
  
  Hope this helps.
  Comment on Kim Seidel's post “Think about the fraction ...”
  (48 votes)
wesley jones
Posted 6 years ago. Direct link to wesley jones's post “i don't really get it why...”
i don't really get it why in the last exercise the slope is -3/2 you ad plus 2 for the change in x but minus 3 for the change in y.
Button navigates to signup pageComment on wesley jones's post “i don't really get it why...”
(33 votes)
Answer
- Neilshet
  Posted 4 years ago. Direct link to Neilshet's post “Because -3/2 is basically...”
  Because -3/2 is basically equal to minus 3 by PLUS 2
  Button navigates to signup page
  (7 votes)
20nlion
Posted 4 years ago. Direct link to 20nlion's post “im having some trouble......”
im having some trouble... anybody have some helpful tips hehehe
Button navigates to signup pageComment on 20nlion's post “im having some trouble......”
(13 votes)
Answer
- owen.esparza
  Posted 5 months ago. Direct link to owen.esparza's post “ligma”
  ligma
  Comment on owen.esparza's post “ligma”
  (1 vote)
Devss
Posted 2 years ago. Direct link to Devss's post “How do I graph a line if ...”
How do I graph a line if the slope isn't provided? Here is what I mean:

y=-x+6

How do I graph it if I do not know the slope? Thanks!
Button navigates to signup pageComment on Devss's post “How do I graph a line if ...”
(13 votes)
Answer
- AniV
  Posted 2 years ago. Direct link to AniV's post “When a variable doesn't h...”
  When a variable doesn't have a variable, it's safe to assume the variable is 1. So, -x would be -1x or -1/1x.
  Hope that makes sense!
  Comment on AniV's post “When a variable doesn't h...”
  (10 votes)
AnnalynnG
Posted 12 days ago. Direct link to AnnalynnG's post “I dont like this”
I dont like this
Button navigates to signup pageButton navigates to signup page
(15 votes)
Answer
- Aubrey Johnson
  Posted 11 days ago. Direct link to Aubrey Johnson's post “me neither but we still h...”
  me neither but we still have to do it
  Button navigates to signup page
  (1 vote)
gjp100
Posted 2 years ago. Direct link to gjp100's post “I don't have a clue on ho...”
I don't have a clue on how to do this
Button navigates to signup pageComment on gjp100's post “I don't have a clue on ho...”
(10 votes)
Answer
- David Severin
  Posted 2 years ago. Direct link to David Severin's post “If you have an equation i...”
  If you have an equation in slope-intercept form, you know both a point (the y intercept) and the slope, so it should be relatively easy to graph especially with a little practice. So if you have y=3x-4, the slope is 3=3/1, the y intercept is (0,-4). We can plot the point by starting at the origin and counting down 4 to get to (0,-4) and put a dot at this point. With a slope of rise (up) 3 over run (right) 1, you get to (0+1,-4+3) which is (1,-1), and a second time (1+1,-1+3) which is (2,2) and you have three points to draw a line through. One more example, if you have y=-3/4x + 2, you have a point (0,2) and a slope of -3/4 (rise down 3 right 4). This gives a second point of (0+4,2-3) or (4,-1) and (4+4,-1-3) or (8,-4) to draw a line. So start with the y intercept, and count the slope from that point.
  Comment on David Severin's post “If you have an equation i...”
  (10 votes)
wesley jones
Posted 6 years ago. Direct link to wesley jones's post “i don't really get it why...”
i don't really get it why in the last exercise the slope is -3/2 you ad plus 2 for the change in x but minus 3 for the change in y.
Button navigates to signup pageComment on wesley jones's post “i don't really get it why...”
(10 votes)
Answer
bail380001
Posted 3 months ago. Direct link to bail380001's post “what if the question is y...”
what if the question is y=x+4
Button navigates to signup pageComment on bail380001's post “what if the question is y...”
(4 votes)
Answer
- Kim Seidel
  Posted 3 months ago. Direct link to Kim Seidel's post “Remember, "x" is the same...”
  Remember, "x" is the same as "1x". So, the slope of the equation is 1 and the y-intercept is (0,4).
  Hope this helps.
  Comment on Kim Seidel's post “Remember, "x" is the same...”
  (10 votes)
2024oshiroc
Posted 3 years ago. Direct link to 2024oshiroc's post “brah can sum1 help me I n...”
brah can sum1 help me I no understand um, Mahaloz
Button navigates to signup pageComment on 2024oshiroc's post “brah can sum1 help me I n...”
(8 votes)
Answer
mukhopadhyayaveri14
Posted 4 months ago. Direct link to mukhopadhyayaveri14's post “I can't understand how to...”
I can't understand how to graph an equation with a fraction y-intercept. Ex: y=2x-1/2
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Kim Seidel
  Posted 4 months ago. Direct link to Kim Seidel's post “Put a point at (0, -1/2)....”
  Put a point at (0, -1/2). It is half-way between 0 and -1.
  Since the slope is 2, you move up 2 units and right 1.
  -- Up 1 unit takes you to 1/2, up 2 units takes you to 1 1/2 (halfway between 1 and 2).
  -- Then, go right 1 unit. You should now be at the point 1 1/2, 1)
  
  Hope this helps.
  Comment on Kim Seidel's post “Put a point at (0, -1/2)....”
  (8 votes)