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?

    (54 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.

      (150 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?

    (28 votes)

    • Karra Wallis

      4 years agoPosted 4 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.

      (38 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!

    (21 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.

      (33 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...”

      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.

      (9 votes)

  • Henry Mays

    a year agoPosted a year 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.

    (15 votes)

    • David Severin

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

      Slope-intercept form introduction | Algebra (article) | Khan Academy (23)

      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.

      (16 votes)

  • deepasaji

    10 months agoPosted 10 months ago. Direct link to deepasaji's post “Why is it called algebra?...”

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

    (5 votes)

    • Rose🌹

      10 months agoPosted 10 months ago. Direct link to Rose🌹's post “There is an overview hist...”

      Slope-intercept form introduction | Algebra (article) | Khan Academy (27)

      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🍀

      (22 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)

    • David Severin

      4 years agoPosted 4 years ago. Direct link to David Severin's post “It is a fixed value, but ...”

      It is a fixed value, but it could possibly look different. So if the slope is 2, you might find points that create a slope of 4/2 or 6/3 or 8/4 or maybe even 1/.5, but each of these will reduce to the same slope of 2.

      (6 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)

  • 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)

  • Gabyscience

    10 months agoPosted 10 months ago. Direct link to Gabyscience's post “Just curious: how do deri...”

    Just curious: how do derivatives differ from slopes?

    (2 votes)

    • David Severin

      10 months agoPosted 10 months ago. Direct link to David Severin's post “Derivatives are instantan...”

      Slope-intercept form introduction | Algebra (article) | Khan Academy (40)

      Derivatives are instantaneous slopes, the line that is tangent to a curve at a given point. Slopes are broader to cover any line, not just tangent lines.

      (10 votes)

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

FAQs

How do you write the equation for the slope intercept? ›

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = 6x + 2, we see that the slope of the line is 6.

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.

How to graph with slope-intercept form? ›

Steps for graphing an equation using the slope and y-intercept:
  1. Find the y-intercept = b of the equation y = mx + b.
  2. Plot the y-intercept. The point will be (0, b).
  3. Find the slope=m of the equation y = mx + b.
  4. Make a single step, using the rise and run from the slope. ...
  5. Connect those two points with your line.

How to find b in slope-intercept form? ›

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept. x and y represent the distance of the line from the x-axis and y-axis, respectively. The value of b is equal to y when x = 0, and m shows how steep the line is.

How to rewrite an equation in slope-intercept form? ›

The equation of a line written in the form y = mx + b is said to be in slope-intercept form. To write an equation in slope-intercept form, you need to isolate y by using the properties of equality. Example: Rewrite the equation 4x - 2y = 12 in slope-intercept form. 4x-2y= 12 -4x -4x -2y = -4x + 12 -2 -2 -2 y=2x-6 1.

How do you express the first equation in slope-intercept form? ›

As we have seen before, you can write the equation of any line in the form of y = mx + b . This is the so-called slope intercept form because it gives you two important pieces of information: the slope m and the y-intercept b of the line. You can use these values for linear interpolation later.

What is the rule for slope and y-intercept? ›

In an equation in slope-intercept form (y=mx+b) the slope is m and the y-intercept is b. We can also rewrite certain equations to look more like slope-intercept form. For example, y=x can be rewritten as y=1x+0, so its slope is 1 and its y-intercept is 0.

How do you put slope and y-intercept in slope-intercept form? ›

The slope-intercept form of the equation of a line is y=mx+b where m is the slope and b is the y-intercept (the point (0,b) where the line intersects the y-axis). If you are given both the slope and y-intercept, simply substitute those numbers for m and b.

What is the simple explanation of slope-intercept form? ›

In math, slope intercept form is a way of writing an equation for a line in the form y = mx + b. The m represents the slope of the line and the b represents the y-intercept. The slope intercept form is used when you want to find either a point on a line or solve for y if you know x.

How many variables does a linear equation have? ›

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.

How to convert an equation to slope-intercept form? ›

Details: To change the equation into slope-intercept form, write it in the form y = m x + b . You want to isolate the y, so the first step is to multiply both sides by 9. Then cancel out the 9's on the right side.

How to write slope-intercept form with two points? ›

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. In this example, we write an equation of the line that passes through the points (-1,6) and (5,-4).

How do you write the equation of a line slope? ›

These are the two methods to finding the equation of a line when given a point and the slope: Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.

Which equation is written in slope-intercept form? ›

y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line. The slope or gradient of a line describes how steep a line is.

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