Slope review | Algebra (article) | Khan Academy (2024)

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

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  • BenGrapentine

    5 years agoPosted 5 years ago. Direct link to BenGrapentine's post “I dont understand this sl...”

    I dont understand this slope thing at all
    can you help me

    (45 votes)

    • Polina Vitić

      5 years agoPosted 5 years ago. Direct link to Polina Vitić's post “You can always figure out...”

      Slope review | Algebra (article) | Khan Academy (4)

      Slope review | Algebra (article) | Khan Academy (5)

      Slope review | Algebra (article) | Khan Academy (6)

      You can always figure out the slope of a line if you have 2 points. If you are not given 2 points, you can find 2 points on the graph and use them to find the slope.

      Here are some good things to know:
      - m = slope
      - (x₁, y₁) = point 1
      - (x₂, y₂) = point 2
      - rise = the difference in the y-values (y₂ - y₁)
      - run = the difference in the x-values (x₂ - x₁)

      In the slope formula, the slope (m) is equal to rise over run:

      m = rise / run
      = (y₂ - y₁) / (x₂ - x₁)

      Let's say we are given a line with points (4, 2) and (6, 1). If we say that point 1 is (4, 2) and point 2 is (6, 1), then:

      x₁ = 4 and x₂ = 6
      y₁ = 2 and y₂ = 1

      Now we just need to plug these values into the slope formula:

      m = rise / run
      = (y₂ - y₁) / (x₂ - x₁)
      = (1 - 2) / (6 - 4)
      = (-1) / 2
      = -1/2

      So the slope (m) is -1/2.

      The main thing to keep track of is which point is (x₁, y₁) and which point is (x₂, y₂). You don't want to mix these up.

      A few tips for graphs of slopes:
      - a perfectly horizontal line has no slope
      - a perfectly vertical line has a slope that is not defined
      - a line that goes upwards (from left to right) has a positive slope
      - a line that goes downwards (from left to right) has a negative slope

      Hope this helps!

      (158 votes)

  • 22cristiansantiagohernandez

    6 years agoPosted 6 years ago. Direct link to 22cristiansantiagohernandez's post “Are you supposed to simpl...”

    Are you supposed to simplify 4.5 by 1.5??

    (45 votes)

  • MarsKitty322

    5 years agoPosted 5 years ago. Direct link to MarsKitty322's post “Why the formula for slope...”

    Why the formula for slope is △ y/ △ x not △ x/ △ y?

    (15 votes)

    • Kim Seidel

      5 years agoPosted 5 years ago. Direct link to Kim Seidel's post “Here are my thoughts...S...”

      Slope review | Algebra (article) | Khan Academy (15)

      Slope review | Algebra (article) | Khan Academy (16)

      Here are my thoughts...
      Slope is a measurement of how steep the line is. The steepness is determined by how fast the line rises/falls. Thus, the predominate measure of importance is the change in Y. If you had △ x/ △ y, then the measurement is more descriptive of how fast the line is moving left/right, which doesn't really describe steepness.

      (33 votes)

  • jaiden.warrens8lol

    6 years agoPosted 6 years ago. Direct link to jaiden.warrens8lol's post “why would you have to do ...”

    why would you have to do the close one said it passes throw 0,5 and 4,2 why can't you just do it were it passes throw the x and y

    (16 votes)

    • Polina Vitić

      4 years agoPosted 4 years ago. Direct link to Polina Vitić's post “You can calculate the slo...”

      Slope review | Algebra (article) | Khan Academy (20)

      Slope review | Algebra (article) | Khan Academy (21)

      You can calculate the slope from the x- and y-intercepts. But in this case, we can't tell exactly what the x-intercept is just from looking at the graph - we can only see that it is somewhere between 6 and 7.

      In order to accurately calculate the slope, we need to use points where we know the exact value. We know the exact value of every point on the grid where the graph lines intersect. So when the line crosses one of those points, we know the exact coordinates for that point on the line.

      For example:
      (-4, 8)
      (0, 5)
      (4, 2)
      (8, -1)

      Any of these points may be used to calculate the slope, and you should get the same answer no matter which 2 points you use.

      Hope this helps!

      (29 votes)

  • Ryin

    5 years agoPosted 5 years ago. Direct link to Ryin's post “How can it be a fraction,...”

    How can it be a fraction, because when I put in a number that we used in class, it said that what I put in was wrong. If you guys could explain that concept to me that would be greatly appreciated

    • Kim Seidel

      5 years agoPosted 5 years ago. Direct link to Kim Seidel's post “The slope of a line is de...”

      Slope review | Algebra (article) | Khan Academy (25)

      The slope of a line is defined as a fraction: rise over run; or (y2-y1)/(x2-x1). So slope is always a fraction. Even if you get a number like 5 as a slope, you need to change it into 5/1 (fraction form) to understand what it means related to the lines movement.

      (16 votes)

  • Keith98A313

    a year agoPosted a year ago. Direct link to Keith98A313's post “This is genuinely so much...”

    This is genuinely so much easier to learn than the way my tutor taught it.

    (21 votes)

    • sweeya.talasila

      7 months agoPosted 7 months ago. Direct link to sweeya.talasila's post “thats kinda mean”

      thats kinda mean

      (5 votes)

  • Space1

    4 years agoPosted 4 years ago. Direct link to Space1's post “how do you graph a linear...”

    how do you graph a linear equation in slope intercept form such as:
    y= 1/2 x - 3

    (10 votes)

    • Kim Seidel

      4 years agoPosted 4 years ago. Direct link to Kim Seidel's post “Slope-intercept form: y=m...”

      Slope review | Algebra (article) | Khan Academy (32)

      Slope-intercept form: y=mx+b where...
      m = the slope
      b = the y-intercept at the point (0, b)

      So, in your equation, your y-intercept = (0, -3).
      Start by graphing that point.
      Then use the slope to find more points.
      Your slope = 1/2. This means from the point (0, -3), go up 1 unit and right 2 units to find the next point. You can repeat this as many times as you want to find points on the line.
      Don't forget to actually draw the line.

      FYI... Search for the leason on graphing from slope intercept form. There is a search bar at the top of all KA screens.

      (18 votes)

  • Colin, Lambert

    5 years agoPosted 5 years ago. Direct link to Colin, Lambert's post “I was wondering if you on...”

    I was wondering if you only have lets say, 2 points on a line, and I was wondering if you could solve for the slope, even if thats all you have

    (8 votes)

    • Martin

      5 years agoPosted 5 years ago. Direct link to Martin's post “Two points would be enoug...”

      Slope review | Algebra (article) | Khan Academy (36)

      Two points would be enough.
      Your points would be (x1, y1) and (x2, y2) then the slope m would be:
      m = y1 - y2 / x1 - x2

      (19 votes)

  • Lillianna White

    3 years agoPosted 3 years ago. Direct link to Lillianna White's post “I just don't understand.....”

    I just don't understand.... how do you tell the slope?

    (11 votes)

    • vm

      3 years agoPosted 3 years ago. Direct link to vm's post “1 coordinate will be x2,y...”

      1 coordinate will be x2,y2.(the 2's and 1's are just to show which coordinate is which not for multipying x)
      Another will be x1,y1.
      Do y2-y1 Divided by x2-x1.

      (2 votes)

  • Akila Kodikara

    5 years agoPosted 5 years ago. Direct link to Akila Kodikara's post “This is confusing me?Any...”

    This is confusing me?
    Any helpp for the last question?

    (10 votes)

    • m971322

      a year agoPosted a year ago. Direct link to m971322's post “To find the slope first f...”

      To find the slope first find two points, for example, I chose (1,2) and (4,4). Remember, slope is rise over run, our rise is 2 and run is 3. So, the slope would be 2/3.

      HOPE THIS HELPS!

      (1 vote)

Slope review | Algebra (article) | Khan Academy (2024)

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