Graphing slope-intercept form (article) | Khan Academy (2024)

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

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  • 682060

    6 years agoPosted 6 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

    (51 votes)

    • Kim Seidel

      6 years agoPosted 6 years ago. Direct link to Kim Seidel's post “Think about the fraction ...”

      Graphing slope-intercept form (article) | Khan Academy (4)

      Graphing slope-intercept form (article) | Khan Academy (5)

      Graphing slope-intercept form (article) | Khan Academy (6)

      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 negative

      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.

      (104 votes)

  • wesley jones

    6 years agoPosted 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.

    (35 votes)

    • Kim Seidel

      6 years agoPosted 6 years ago. Direct link to Kim Seidel's post “When you have a negative ...”

      Graphing slope-intercept form (article) | Khan Academy (10)

      Graphing slope-intercept form (article) | Khan Academy (11)

      Graphing slope-intercept form (article) | Khan Academy (12)

      When you have a negative slope, like -3/2 then one of the numbers must be negative (remember, negative divided by positive = negative; and positive divided by negative = negative).

      So, when you interpret the slope of -3.2...
      1) You can do -3 for change in Y (move down 3 units) and +2 for X (move right 2 units). OR... 2) You can do +3 for change in Y (up 3 units) and -2 for X (move left 2 units).
      Hope this helps.

      (80 votes)

  • 20nlion

    4 years agoPosted 4 years ago. Direct link to 20nlion's post “im having some trouble......”

    im having some trouble... anybody have some helpful tips hehehe

    (16 votes)

    • Zachary Heaton

      9 months agoPosted 9 months ago. Direct link to Zachary Heaton's post “place you first point on ...”

      place you first point on the y axis +/-. Then turn the slope into a fraction.
      Slope: The positive or negative sign determine if the line goes up or down from the y intercept. Based on that, going left to right, if it is a negative travel down the numerator, travel right the denominator.

      Y=27/3x+1 Place first point on y axis at positive 1. Then travel up 27, then go right 3. Simplified, you would go up 9, and right 1.

      (3 votes)

  • gjp100

    3 years agoPosted 3 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

    (15 votes)

    • David Severin

      3 years agoPosted 3 years ago. Direct link to David Severin's post “If you have an equation i...”

      Graphing slope-intercept form (article) | Khan Academy (19)

      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.

      (14 votes)

  • Devss

    3 years agoPosted 3 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!

    (14 votes)

    • Ani V

      3 years agoPosted 3 years ago. Direct link to Ani V's post “When a variable doesn't h...”

      Graphing slope-intercept form (article) | Khan Academy (23)

      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!

      (11 votes)

  • Envy

    3 years agoPosted 3 years ago. Direct link to Envy's post “Not to be that person but...”

    Not to be that person but like When am I reallyyyyyyyyyyyy going to use this in everyday life?

    (11 votes)

    • Logan.Lewis

      a year agoPosted a year ago. Direct link to Logan.Lewis's post “my teacher says yes but h...”

      my teacher says yes but he is a goober so I don't know

      (3 votes)

  • wesley jones

    6 years agoPosted 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.

    (9 votes)

  • mukhopadhyayaveri14

    a year agoPosted a year 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

    (5 votes)

    • Kim Seidel

      a year agoPosted a year ago. Direct link to Kim Seidel's post “Put a point at (0, -1/2)....”

      Graphing slope-intercept form (article) | Khan Academy (32)

      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.

      (11 votes)

  • bail380001

    a year agoPosted a year ago. Direct link to bail380001's post “what if the question is y...”

    what if the question is y=x+4

    (4 votes)

    • Kim Seidel

      a year agoPosted a year 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.

      (9 votes)

  • 563080

    6 years agoPosted 6 years ago. Direct link to 563080's post “what is the difference be...”

    what is the difference between zero slope and no slope.

    (1 vote)

    • Ian Pulizzotto

      6 years agoPosted 6 years ago. Direct link to Ian Pulizzotto's post “Zero slope means the slop...”

      Graphing slope-intercept form (article) | Khan Academy (39)

      Zero slope means the slope is defined as zero, but no slope means the slope is undefined. A horizontal line has zero slope, but a vertical line has no slope.

      Have a blessed, wonderful day!

      (12 votes)

Graphing slope-intercept form (article) | Khan Academy (2024)

FAQs

What is the answer in slope-intercept form? ›

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.

How do you solve a graph in slope-intercept form? ›

The equation is written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept.
  1. Step 1: Find the slope and the y-intercept of the line:
  2. Step 2: Graph the y-intercept:
  3. Step 3: Find another point on the line using the slope:
  4. Step 4: Draw a line that passes through the points:

What is the slope and intercept in a graph? ›

What is the Slope Intercept Form of a Line? The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers. The slope, m, represents the steepness of a line.

What is the slope intercept formula *? ›

Slope-intercept form (y=mx+b) of linear equations highlights the slope (m) and the y-intercept (b) of a line. Watch this video to learn more about it and see some examples.

How to calculate a 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.

What is the formula for the slope of a graph? ›

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. Created by Sal Khan and Monterey Institute for Technology and Education.

How to find y-intercept with slope? ›

Once the slope has been identified, write a linear equation in slope-intercept form (y=mx+b). Using one set of coordinates (x,y) and the slope m, rewrite the equation by substituting the appropriate values for x, y, and m. Then, solve the equation for b to identify the y-intercept.

How to graph an intercept? ›

Graphing Lines Using Intercepts
  1. Solution:
  2. Step 1: Find the x- and y-intercepts.
  3. Step 2: Plot the intercepts and draw the line through them. Use a straightedge to create a nice straight line. Add an arrow on either end to indicate that the line continues indefinitely in either direction.
  4. Answer:
  5. Figure 3.3.
Oct 6, 2021

How do you write 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 to convert to slope-intercept form? ›

To change the equation into slope-intercept form, write it in the form y = m x + b .

How to solve 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 do you graph slope-intercept form? ›

To graph a linear equation in slope-intercept form, we can use the information given by that form. For example, y=2x+3 tells us that the slope of the line is 2 and the y-intercept is at (0,3). This gives us one point the line goes through, and the direction we should continue from that point to draw the entire line.

What is an example of a slope? ›

For example, the equation y - 3 = 2(x - 1) is in the point-slope form and the slope is 2 since the 2 is in the m spot. The equation y = 3x + 4 is in the slope-intercept form with a slope of 3 since the 3 is in the m spot. For parallel lines, the slope is the same.

What's rise over run? ›

Rise over run is the inclination of a line in the coordinate axis. The rise is computed along the vertical y-axis and the run is computed along the horizontal x-axis and the rise over run is expressed as a ratio, where the rise along the y-axis is divided by the run along the x-axis.

What is the slope of the line answer? ›

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).

What is the intercept in slope-intercept form? ›

How do you find the X Intercept in y = mx + b? Here, y = mx + b is the slope-intercept form that can be used to identify the x and y-intercepts. The x-intercept is found by setting y = 0. On substituting the value of y =0, it gives the x-intercept value at which the line crosses the x-axis.

What is an example of intercept form? ›

Intercept Form of Equation of a Line: x/a + y/b = 1. Here x, y, are the variables in the equation, a, b, are the x-intercept, and the y-intercept in the equation. This equation has a slope of -b/a.

References

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