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# Slope-intercept form from a table

CCSS.Math:

## Video transcript

a line goes through the following points and the equation of that line is written in y equals MX plus B form also known as slope-intercept form what is the equation of the line so the first thing we want to think about what is the slope of this line what is M here so what is our change in Y for given change in X so this is an interesting example here and I encourage you to pause the video and try it out yourself because no matter how much we change X Y is not changing Y is a constant - so your change in Y between any two points is going to be zero it doesn't matter what your change in X is your change in X could be 1 your change in X could be four your change in Y is always zero so Y is not changing as you change X so your slope for this for this relationship is actually zero Y is equal to zero X + and then you could you could just realize that this is this the equation of this is just that Y is always equal to 2 so it's zero X + 2 which is the same thing as Y is equal to 2 you could substitute back in you could say ok well Y is equal to zero X plus B that means that Y is equal to B well Y is always equal to 2 no matter what pick what no matter what thing do pick so B is equal to 2 so either way you this just boils down to Y is equal to 0 X plus 2 or Y is just equal to 2 let's do another one of these maybe one where the Y is actually changing so here the Y is clearly the Y is actually changing so let me copy and paste this so let me copy and paste this one put it on my scratch pad and we could work it out so let's stick it right over here and then we are told we are told a line goes through the file ok so the same thing the line goes through these points what's the equation of the line so the main idea here is you only need two points for an equation of line they've given us more than necessary so I'd like to pick the two points that make things a little bit simpler so I'll pick the point 4 2 + 7 0 I just picked those two points because they have nice clean numbers associated with it so what is our change in X here so our change in X here if we go from four to seven our chin X is equal to three change in X is equal to three and what's our change in Y here so we went up from four to seven we increased by three our Y decreased by two change in Y is equal to negative two so our slope which is equal to change in Y over change in X is equal to negative two thirds and if you wanted to relate that to the formulas that you normally see for slope you're just looking at your end point so this is y2 minus y1 which is negative 2 over x2 minus x1 which is 7 minus 4 but that just boils down to negative 2/3 and it's and so our equation is going to be Y is equal to negative 2/3 X plus B so let's substitute one of these points in here to figure out what our B must be and once again I like let's see I want to figure out something where this is going to become nice and clean but this isn't going to be clean really clean for any of these numbers right over here if this if we had a 3 for X or 6 for X or a 0 for X then things would work out nicely but they don't give us any of those so let's just try let's just try the 7 and this is 0 so when X is equal to 0 sorry when X is equal to 7 Y is equal to 0 so when X is equal to 7 I'll just do the same color Y is equal to 0 so 0 is equal to negative 2/3 times 7 plus B or 0 is equal to negative 14 over 3 3 plus B add 14 over 3 to both sides you get 14 over 3 is equal to B so this is going to be y is equal to negative let me go back to the other screen so it's y is equal to negative 2/3 X plus 14 over 3 so let me do that so Y is equal to Y is equal to negative 2/3 X negative 2/3 X plus 14 over 3 14 over 3 let's check our answer we got it right