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Graphing using intercepts (old)

An old video of Sal where he draws the line y=3x-9 by finding its x- and y-intercetps. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • duskpin ultimate style avatar for user Talia
    Do we always plug in zero for the variable? I have been having a lot of trouble with these questions and I watched all these videos, and every time Sal plugs in 0 for the variable and proceeds through the equation. Is this something that happens in every problem?
    (8 votes)
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    • blobby green style avatar for user Nancy Erle
      When you are talking about the x intercept, where it crosses the x axis, you do not have to go up or down to get to that point; so your y value is zero.
      When you are talking about the y intercept, where it crosses the y axis, you do not have to go left or right; so your x value is zero.

      When you plug in a value for one variable you can use the equation to solve for the other, this creates a point that makes the equation true. which means it is a point on the line.

      You can plug any value in for x or y with LINEAR equations (other types of equations will have domain and range restrictions), but the easiest value to plug in almost all cases is zero. Most students, when asked to graph lines in two variables, automatically start by drawing the x and y axis. Since your Intercepts lie on these axis, plotting the x and y intercepts comes naturally.

      Other points can be found by plugging in various numbers for x and then solving for y, like you would in a table of values approach to graphing. With linear equations it only takes two points to graph the line. Or a point (preferably the y intercept) and the slope (which generates more points -so you have at least two).
      (2 votes)
  • aqualine ultimate style avatar for user Lost
    what would be an equation that passes through the point (3, 2) and creates a system of equations with 10x + 5y = 15 that has no solutions.
    (3 votes)
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    • piceratops ultimate style avatar for user Justin150
      Well, we know that for a system of linear equations to have 0 solutions, their graphs must be parallel. In other words, they have the same slope.
      If we change 10x +5y = 15 into slope-intercept form, we get y = -2x +3. So the slope is -2, and the slope of the line we must find is also -2.
      Given the point (3,2), we can use Point-Slope form to write the equation: y-2=-2(x-3). Written in slope intercept form, this is y = -2x +8, and written in standard form, it is 2x + y = 8.
      (4 votes)
  • blobby green style avatar for user Candice Grant
    so when finding coordinates do we use the same strategy to plot on the graph
    for example y= -1/3x+8 how would its graph look
    (2 votes)
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    • leafers ultimate style avatar for user Caleb Bibb
      I can use the b in your equation (y=mx+b) to know the y-intercept right off the bat. Then from there I know that m= rise/run. So I know that the next point will be 1 unit down and 3 units to the right. This graph will eventually be a line going down from left to right with a smooth slope.
      (3 votes)
  • blobby green style avatar for user William JT Day
    Ok, My questions is related to this.........If a graphed line is on the y axis and meets x at points (0,0) or a vertical line basically running on the y axis. What would the linear inequality equation be......? I assumed its y=x.....even my teacher does not know how!
    (2 votes)
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    • hopper cool style avatar for user Chuck Towle
      William,
      The linear equation would be x=0
      It could also be written as x=0y or x=0y+0
      No matter what number you put in for y, x is always 0 which gives you a line on the y axis.

      Note that this cannot be written as a function of x because one x value results in more than one answer for y (In fact you have an infinite number of y value when x is 0)
      Also note that if you take two points on the line and find the slope as (change in y)/(change in x) you get a 0 for the denominator. Any fraction with a 0 in the denominator is undefined. So the slope of the line x=0 is undefined. Any vertical line will have an undefined slope.

      I hope that helps make it click for you.
      (2 votes)
  • blobby green style avatar for user Becky Sindlinger
    At , i need to practice!! I don't need a video!
    (1 vote)
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  • male robot hal style avatar for user 20yuankaiwen
    Using information from a graph how would you find a graph using slop and y-intercept?
    (2 votes)
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  • female robot ada style avatar for user Samantha
    If the x-intercept means that y=0, does that mean that the y-intercept would mean x=0? Is it always like that?
    (2 votes)
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    • blobby green style avatar for user InnocentRealist
      Yes always.
      For a straight line y = mx + b, for every number on the x axis the equation of the line gives you the y value (mx+b) on the line. the y you get for x=0 is called the "y intercept" (m(0) + b).

      If you think of y as an independent variable, you can see that the same line "y=mx+b" has a different slope in relation to the y axis (solve "y = mx + b" for x to get "x = (1/m)y - b/m" to get this slope.). Now, for every value of y there is a value of x, = (1/m)y - b/m, on the line, and the x you get for y = 0, = (1/m)*0 - b/m, is the x-intercept.
      But you don't have to go through all this - you can just use "y = mx + b", set y=0 and solve "mx+b = 0", which does the same thing..
      (2 votes)
  • piceratops seedling style avatar for user rama dalavayi
    x-intercept of 4 and a y-intercept of 3, find the slope of a parallel line and the slope of a perpendicular line
    (2 votes)
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    • blobby green style avatar for user zhangd
      Parallel Line Slope: -3/4
      Perpendicular Line Slope: 4/3

      The Parallel Line's slope is equivalent to the slope of the given line, and the perpendicular line's slope is the negative reciprocal of the given line's slope, i.e. if the given line's slope is "m", then the perpendicular line's slope is "-1/m".
      (1 vote)
  • spunky sam blue style avatar for user tsj2001
    for a function equation (y=mx + b)
    why do we have to find the y intercept and not the x intercept.
    (2 votes)
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  • blobby green style avatar for user mjbpmrmjb
    So if the line never hits the x or y axis then is there just no intercept?
    (2 votes)
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    • leafers ultimate style avatar for user Rob Dresdow
      Assuming it is coplanar, it will always intercept at least one axis, but if it is parallel to one of the axes, it will only have one intercept, at least in regard to the axis with which it is perpendicular. For example, if the line is parallel to the x axis, it will only have a y intercept, and vice versa.
      (1 vote)

Video transcript

Identify the x and y-intercepts of the line y is equal to 3x minus 9. Then graph the line. So the x-intercept, I'll just abbreviate it as x-int, that is where the line intersects the x-axis. So where it intersects the x-axis. Remember, this horizontal axis is the x-axis. So when something intersects the x-axis, what do we know about its coordinate? Its x-value could be anything, but we know it's y-value is 0. If we're intersecting, if we're sitting on the x-axis someplace, that means that we haven't moved in the y-direction. That means that y is 0. So this means, literally, that y is 0. So we need to find the x-value defined by this relationship when y is equal to 0. Similarly, when we talk about the y-intercept, I'll do it down here-- when we talk about the y-intercept, what does that mean? Well, y-intercept means-- so this is the y-axis right over here running up and down. The y-intercept is the point at which the line intercepts the y-axis. So what's going on? If we're at the y-axis, our y-value could be anything depending on where we intersect the y-axis. But we know that we haven't moved to the right or the left. We know that our x-value is 0 at the y-intercept. So over here, our x-value is going to be 0. And to find the actual point, we just have to find the corresponding y-value defined by this relationship or this equation. So let's do the first one first. The x-intercept is when y is equal to 0. So we set y is equal to 0, and then we'll solve for x. So we get 0 is equal to 3x minus 9. We can add 9 to both sides of this equation to isolate the x-term. So we get 9 is equal to 3x. These cancel out. We could divide both sides by 3. Divide both sides by 3. We get 3 is equal to x or x is equal to 3. So the point y is equal to 0, x is equal to 3 is on this line. And let me put it in order. x-coordinate always goes first. So it's 3 comma 0. So this is the origin. 1, 2, 3 is right over here. That is 3 comma 0. This right here is the x-intercept. And remember, notice that point lies on the x-axis, but the y-value is 0. We haven't moved up or down. When you think x-intercept, you say, OK, that means my y-value is 0. So I have to solve for the x-value. Now we do the opposite for the y-intercept. And the y-intercept, we're sitting on this line, x-value must be 0. So let's figure out what y is equal to when x is equal to 0. So y is equal to-- I want to do it in that pink color. y is equal to-- y is equal to 3 times-- x is 0 now. 3 times 0 minus 9. Well, 3 times 0 is just 0. So 0 minus 9. Well that's, just equal to negative 9. So we have the point 0 comma negative 9. So when x is 0, we go down 9 for y. 1, 2, 3, 4, 5, 6, 7, 8, 9. So right there is the point 0 comma negative 9. Notice, it sits on the y-axis. That's why it's the y-intercept. And the x-value is 0. We haven't moved to the left or right. All you need is two points for a line, so we're now ready to graph. We essentially just have to connect the dots. So it's going to look something like this. It's going to look something-- our line. I don't have a good line tool, so I'm going to try my best to draw it nicely-- is going to look something like that. And you just keep going. You just keep going. You want to do a straight line. So it just keeps going on and on and on like that. It just keeps going. And I could keep going all the way in that direction, and then-- but then my line doesn't look as straight all of a sudden. I think you get the general idea. I can keep going like that, and then keep going like that. I don't have a nice ruler to do it with. And we're done.