Slope-intercept form introduction | Algebra (article) | Khan Academy (2024)

Learn about the slope-intercept form of two-variable linear equations, and how to interpret it to find the slope and y-intercept of their line.

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  • Patrice Abbee

    6 years agoPosted 6 years ago. Direct link to Patrice Abbee's post “What if m=0?”

    What if m=0?

    (56 votes)

    • Admiral Betasin

      6 years agoPosted 6 years ago. Direct link to Admiral Betasin's post “If the slope is 0, is a h...”

      Slope-intercept form introduction | Algebra (article) | Khan Academy (4)

      Slope-intercept form introduction | Algebra (article) | Khan Academy (5)

      Slope-intercept form introduction | Algebra (article) | Khan Academy (6)

      If the slope is 0, is a horizontal line. It makes sense if you think about it. Each time we increase one x, increase y by 0.

      (151 votes)

  • faith reinhold

    5 years agoPosted 5 years ago. Direct link to faith reinhold's post “how do you find the slope...”

    how do you find the slope and intercept on a graph?

    (30 votes)

    • Karra Wallis

      5 years agoPosted 5 years ago. Direct link to Karra Wallis's post “To find the y-intercept, ...”

      Slope-intercept form introduction | Algebra (article) | Khan Academy (10)

      Slope-intercept form introduction | Algebra (article) | Khan Academy (11)

      To find the y-intercept, find where the line hits the y-axis. To find the x-intercept (which wasn't mentioned in the text), find where the line hits the x-axis. To find the slope, find two points on the line then do y2-y1/x2-x1 the numbers are subscripts.
      Hope that helped.

      (43 votes)

  • Varahi

    7 years agoPosted 7 years ago. Direct link to Varahi's post “I dont understand this wh...”

    I dont understand this whole thing at all PLEASE HELP!

    (24 votes)

    • Kim Seidel

      7 years agoPosted 7 years ago. Direct link to Kim Seidel's post “The slope-intercept form ...”

      Slope-intercept form introduction | Algebra (article) | Khan Academy (15)

      Slope-intercept form introduction | Algebra (article) | Khan Academy (16)

      The slope-intercept form of a linear equation is where one side contains just "y". So, it will look like: y = mx + b where "m" and "b" are numbers.
      This form of the equation is very useful. The coefficient of "x" (the "m" value) is the slope of the line. And, the constant (the "b" value) is the y-intercept at (0, b)
      So, if you are given an equation like: y = 2/3 (x) -5
      We can tell that the slope of the line = 2/3 and the y-intercept is at (0, -5)
      Hope this helps.

      (36 votes)

  • Carson Payne

    7 years agoPosted 7 years ago. Direct link to Carson Payne's post “how does an equation resu...”

    how does an equation result to an answer?

    (23 votes)

    • hanco*ckandrewj

      3 years agoPosted 3 years ago. Direct link to hanco*ckandrewj's post “The equation results in h...”

      Slope-intercept form introduction | Algebra (article) | Khan Academy (20)

      The equation results in how to graph the line on a graph. If they give you the x value then you would plug that in and it would tell you the answer in y.

      (10 votes)

  • Henry Mays

    2 years agoPosted 2 years ago. Direct link to Henry Mays's post “Why should I learn this a...”

    Why should I learn this and what can I use this for in the future.

    (16 votes)

    • David Severin

      2 years agoPosted 2 years ago. Direct link to David Severin's post “slopes are all over the p...”

      Slope-intercept form introduction | Algebra (article) | Khan Academy (24)

      slopes are all over the place in the real world, so it depends on what you plan to do in life of how much you use this. Art, building, science, engineering, finance, statistics, etc. all use linear functions.

      (18 votes)

  • Vector Inc.

    4 years agoPosted 4 years ago. Direct link to Vector Inc.'s post “Is it ever possible that ...”

    Is it ever possible that the slope of a linear function can fluctuate? Or is the slope always a fixed value?

    (10 votes)

    • Kim Seidel

      4 years agoPosted 4 years ago. Direct link to Kim Seidel's post “A linear functions create...”

      Slope-intercept form introduction | Algebra (article) | Khan Academy (28)

      A linear functions creates a straight line. So, the slope is always a fixed value. If the slope could fluctuate, then you wouldn't have a straight line graph. The graph would be curved, or V-shaped.

      (14 votes)

  • deepasaji

    a year agoPosted a year ago. Direct link to deepasaji's post “Why is it called algebra?...”

    Why is it called algebra? Is it Greek or something?

    (7 votes)

    • Rose🌹

      a year agoPosted a year ago. Direct link to Rose🌹's post “There is an overview hist...”

      Slope-intercept form introduction | Algebra (article) | Khan Academy (32)

      There is an overview history video in Algebra 1 that explains this better than I can but basically Algebra is a Medieval Latin short hand for the title of the first book explaining these principals.
      It was called "al-mukhtasar fi hisab al-jabr wa al-muqabala", which is Arabic for "the compendium on calculation by restoring and balancing".
      Here's the link to the vid if you want to explore further: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:algebra-overview-history/v/origins-of-algebra
      Hope I answered your question well! Best of luck learning🍀

      (24 votes)

  • kendellnoble2002

    7 years agoPosted 7 years ago. Direct link to kendellnoble2002's post “say you have a problem li...”

    say you have a problem like (3,1) slope= 4/3. how would you work that out

    (3 votes)

    • Rei

      4 years agoPosted 4 years ago. Direct link to Rei's post “Pretty late here, but for...”

      Pretty late here, but for anyone else reading, I'll assume they meant how you find the slope intercept using only these values.

      Since we know the slope is 4/3, we can conclude that: y = 4/3 * x ... But what is the constant, the y axis intercept point?

      You can solve for it by doing: 1 = 4/3 * 3 + c... We know the values for x and y at some point in the line, but we want to know the constant, c. You can solve this algebraically.
      1 = 4/3 * 3 + c
      1 = 4 + c
      1 - 4 = 4 - 4 + c
      -3 = c

      The slope intercept equation is: y = 4/3 * x - 3

      The y axis intercept point is: (0 , -3)

      I just started learning this so if anyone happens across this and spots an error lemme know.

      (8 votes)

  • Karina Rutann

    2 years agoPosted 2 years ago. Direct link to Karina Rutann's post “I am so lost I need help ...”

    I am so lost I need help :((

    (6 votes)

    • David Severin

      2 years agoPosted 2 years ago. Direct link to David Severin's post “The start of the lesson s...”

      The start of the lesson states what you should have some understanding of, so the first question is do you have some understanding of these two concepts?
      "You should know what two-variable linear equations are. Specifically, you should know that the graph of such equations is a line. If this is new to you, check out our intro to two-variable equations.
      You should also be familiar with the following properties of linear equations: y-intercept and x-intercept and slope."
      If these are an issue, you need to go back and review these concepts. If you understand these, then you need to be more specific on where you are struggling. This is just an intro, so it is basically identifying slope and intercept from an equation. Which checks do not make sense?

      (4 votes)

  • Alex

    a year agoPosted a year ago. Direct link to Alex's post “How do I find the x inter...”

    How do I find the x intercept?

    (3 votes)

    • Kim Seidel

      a year agoPosted a year ago. Direct link to Kim Seidel's post “You use y=0 in the equati...”

      You use y=0 in the equation and calculate "x"

      (8 votes)

Slope-intercept form introduction | Algebra (article) | Khan Academy (2024)

FAQs

How do you write an equation in slope-intercept form? ›

Given two points on a line, we can write an equation for that line by finding the slope between those points, then solving for the y-intercept in the slope-intercept equation y=mx+b.

How do you introduce the slope and y-intercept? ›

The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y.
  1. The slope indicates the rate of change in y per unit change in x.
  2. The y-intercept indicates the y-value when the x-value is 0.

What is the summary of the slope-intercept form? ›

The slope-intercept form of a line is a way of writing the equation of a line so that the slope of the line and the y-intercept are easily identifiable. The slope is the steepness of the line, and the y-intercept is the place the line crosses the y-axis.

What is the intercept form of the line? ›

The intercept form of the equation of a line is x/a + y/b = 1. This is one of the important forms of equations of a line. Also, the sign of the intercepts in this equation helps us to know the location of the line with respect to the coordinate axes.

How to simplify slope-intercept form? ›

The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Rewrite in slope-intercept form. Subtract 3x 3 x from both sides of the equation. Divide each term in 4y=−5−3x 4 y = - 5 - 3 x by 4 4 and simplify.

Why is the slope-intercept form important? ›

The slope-intercept form helps understand how slope and y-intercept changes affect a linear relationship's behavior, making it helpful in modelling real-life scenarios like budget planning or sales forecasting.

What does the slope intercept equation tell us? ›

Slope-intercept form (y=mx+b) of linear equations highlights the slope (m) and the y-intercept (b) of a line.

What is the meaning of the intercept form? ›

The two-intercept form of the equation of a straight line that intersects the X-axis at (𝑎,0) and the Y-axis at (0,𝑏) is. x a + y b = 1. The intercept form allows us to visualize the position of the line and its relationship with the coordinate axes based on the signs of the intercepts.

How do you use intercept form? ›

To write a quadratic function in intercept form,
  1. Find the x-intercepts. ...
  2. Find one other point that the graph passes through. ...
  3. Substitute the x-intercepts for p and q in intercept form y = a(x – p)(x – q).
  4. Substitute the point for x and y.
  5. Solve for a.
  6. Write the function by substituting p, q, and a into intercept form.

How to figure out slope? ›

The slope, or steepness, of a line is found by dividing the vertical change (rise) by the horizontal change (run). The formula is slope =(y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of two points on the line.

Which equation is written in slope-intercept form? ›

The equation, y = mx + b, is the slope-intercept form of a straight line. Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.

How do you write an equation in slope-intercept form of the trend line? ›

To calculate the trend line for the graph of a linear relationship, find the slope-intercept form of the line, y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept.

How do you write an equation given the slope and a point? ›

Point-slope form: y-a = m(x-b). For example, your slope (m) is 3 and your point (a,b) is 9,10. You would substitute your y-coordinate for a, and your x- coordinate for b. Your new equation would look like this: y-10 = 3(x-9).

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