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# Graphing using intercepts (old)

## 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 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 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 we are in that point lies on the x axis but the y-value is zero we haven't moved up or down when you think x intercept you say ok that means my y-value is zero 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 wanted 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 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 drive my best to draw it nicely is going to look something 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 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