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.

      (17 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 introduce the slope and y-intercept? ›

The slope indicates the rate of change in y per unit change in x. 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 slope intercept method? ›

The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope intercept form is given as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the y-intercept.

What is the slope of y? ›

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. The slope of the line is also called the gradient.

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

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 a standard form with slope and y-intercept? ›

Then write an equation in slope-intercept form (y=mx+b) and substitute in the x and y values for one of the points to find the y-intercept (b). Then convert to standard form (Ax+By=C) by subtracting the (mx) term from each side. In standard form, A, B, and C should be integers, so eliminate any fractions or decimals.

How do you explain intercept form? ›

The intercept form of the equation of a line is x/a + y/b = 1. The intercept form of the equation of a line makes the x-intercept of 'a' units, and the y-intercept of 'b' units. Based on the sign of the intercepts we can find the quadrants through which the line passes through.

What is slope-intercept form simplified? ›

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.

Why is the slope-intercept form important? ›

Why is the slope-intercept form important in real-life scenarios? 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 are the characteristics of slope-intercept form? ›

An equation in slope-intercept form of a line includes the slope and the initial value of the function. The initial value, or y-intercept, is the output value when the input of a linear function is zero. It is the y-value of the point where the line crosses the y-axis.

What is the point slope intercept form? ›

The point slope formula is of the form y − y1 1 = m (x − x1 1 ) whereas the slope-intercept formula is of the form y = mx + b, where 'm' is the slope, 'b' is the y-intercept, and (x1 1 , y1 1 ) is a point on the line. To derive the slope-intercept formula from point slope formula, we will just have to solve it for y.

What does a slope tell you? ›

The slope of a line represents how the y-axis values change compared to the numbers on the x-axis. This is also called the rate of change. We have also seen the following: The larger the slope = the steeper the line, or in other words, the greater the rate of change.

How to interpret slope and intercept? ›

The slope represents the change in y for any 1 unit change in x. The intercept, also known as the y-intercept, is where the line of best fit intersects the y-axis. It represents the initial condition or starting point of the data.

How to determine slope? ›

Percent of slope is determined by dividing the amount of elevation change by the amount of horizontal distance covered (sometimes referred to as "the rise divided by the run"), and then multiplying the result by 100.

How to identify slope and y-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 = − 3 x + 5 , we see that the slope of the line is − 3 .

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

The equation for slope-intercept form is: y=mx+b In this form, m is the slope of the line and the b is the y-intercept.

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