Intercepts from a table

the following table values represents points X comma Y on the graph of a linear function determine the y intercept of this graph so just as a reminder of what the y intercept even is if you imagine a linear function or a line if we're graphing it if we imagine a line so let's say that is our line right over there this is our y-axis this is our x-axis the y intercept is where we intersect the y-axis now what do we know about the y intercept well at the y intercept X is going to be equal to zero so this is the point 0 comma something and when so when people are talking about what is your y intercept they're usually saying well what is the what is the y coordinate when x equals 0 so we're really trying to figure out what is the y coordinate when x equals 0 so we know the x coordinate when y is equal to 0 so this is actually the x intercept so this point right over here is the point 2 comma 0 so when people say x intercept that's the that's the x coordinate when y equals 0 well they already they gave us the x intercept so that right over there is the X the x intercept but what's the y intercept what is the Y value when x equals 0 let's see they give us what happens to Y when X is negative 2 when it's 1 when it's 2 when it's 4 so maybe we can backtrack from one of these to get back to what happens when X is equal to 0 so let me rewrite let me rewrite through this table so I can give ourselves a little bit more breathing room so let's say we have X and we have Y X and Y and they already tell us that when X is negative 2 X is negative 2 y is 8 and I actually want to think about what happens when X is negative 1 when x is 0 then they tell us when X is 1 Y is 2 when X is 2 y is 0 this right over here is the x-intercept when X is 4 y is negative 4 so they skip 2 right over here y is negative 4 so let's just see how Y changes with respect to changes in X so when we go here when X changes by 1 so when X changes by 1 why goes down by two and it's aligned so it's going to have a constant rate of change of Y with respect to X so similarly when x increases by 1 Y is going to decrease by 2 so Y is going to be 6 here when x increases by 1 again y is going to decrease by 2 so we're going to get to 4 we see it works because if we increase by 1 again then it is indeed the case that Y decreased by 2 and you see here when we increase X by 2 then Y decreases at twice the rate because now we didn't just increase by 1 we increased by 2 so now Y is going to decrease by 4 and what's constant here is your change in Y over your change in X when X D when x increases by 1 Y decreases by 2 when x increases by 2 Y decreases by 4 either way either either way you think about it your change in Y for unit change in X is going to be equal to negative 2 but anyway we actually answered the question before without even realizing it when we filled in all of these values what is the Y value when x equals 0 well the Y value is 4 so the y intercept here is 4 we didn't really graph this to scale it would actually look a little bit more like this if we were to try to graph it properly so this right over here is 4 this right over here is 2 and our line looks something like this our line will look something like something like that