Hey everyone, it's Justin again.
In this video, we're gonna be learning how to find intercepts from a table of values.
With a graph, you just look at the axis and you can find the intercepts.
With equations, you plug in 0 for one variable and solve for the other.
But what if all you were given was a table of values?
In this case, it will take a little more thinking and logic but it can still be done very easily.
In this example, here is the x-intercept, and here is the y-intercept.
Well, how do we know that?
Remember the defining feature of intercepts: one of the values is 0.
This is how we'll find the intercepts from a table— find the points where either coordinate
is 0.
But it's not always that simple.
This table doesn't have a 0 for x or y.
But we can find them by continuing the pattern.
First, we need to find the slope.
You'll see why in a moment.
Using the top two points, we can get that the change in y is plus 5 and the change in
x is plus 12, so the slope is 5 over 12.
This tells us the pattern is that y goes up by 5 and that x goes up by 12.
We can use this pattern to expand the table.
Look at the bottom.
If we add 12 to the x value twice, we get 0.
Any time x goes up by 12, y goes up by 5.
So, here's the next two y values.
So, the y-intercept is (0, 30).
To get the x-intercept, we have to add rows to the top of the table because we have to
reverse the y until it hits 0.
Luckily, we only have to reverse it once by subtracting 5.
If we subtract 5 from the y, we also subtract 12 from the x, so here is the x-intercept
(-72,0).
Here's another example.
Right off the bat, we can already see the x-intercept.
The y-intercept is hidden though, so let's find the pattern.
The slope is -1 over 2, so every time y goes down by 1, x goes up by 2.
In order to find the y-intercept, we need to keep the table going until the x is 0.
Then, we use the pattern.
Whenever the x goes up by 2, the y goes down by 1.
The y-intercept is (0, -3).
For our next example, neither intercept is shown so we'll have to search for both of
them.
The slope is -10 for the y and -15 for the x, which reduces to 2 over 3.
So any time the y goes up by 2, the x goes up by 3, so let's try extending the table
down.
We keep the pattern and subtract 2 from the y, the x has to subtract 3 but, oh, the x
and the y just got further from 0.
So, we don't need to add rows to the bottom as it turns out.
We need to add rows to the top.
Since -10 is closer to 0, let's try to find the x-intercept first.
To go from -10 to 0, we add 10 to the y value, but then we need to add an appropriate amount
to x.
The slope said 3 x's for every 2 y's, so how many times do we add 2 to the y here?
Well, adding 10 is like adding 2, five times.
So if we added 2 five times to the y, we should add 3 five times to the x.
So then, if y goes up by 10, x has to go up by 15.
To find the y-intercept, we'll do the same thing again.
For the x to be 0, we need to add 30.
Adding 30 to the x is like adding 3 ten times, so we need to add 2 times 10, or 20, to the
y.
So the x-intercept is (-30, 0) and the y-intercept is (0, 20).
Let's do one more example.
This will be the hardest one by far, but with everything
we know now, it'll still be a breeze.
First, if we check the slope between any two points
here, we will get positive 4 over -16, which is -1/4.
This means that when the y goes down by 1, the x goes up by 4.
If we look at the table, we see that the x will be 0 in between 4 and -12, the y will
be 0 in between -2 and 2.
So, let's look at the x-intercept first, where the y is 0.
To go from -2 to 0, we had to add 2 to the y.
Adding 2 is like adding 1 twice, so according to the slope we need to subtract 4 twice from
the x, meaning we subtract 8.
For the y-intercept, now I'm going from -12 to 0 means that we added 12.
Since we added 4 three times to the x, the slope says we should subtract 1 three times
from the y, so the x-intercept is (12, 0) and the y-intercept is (0, 3).
Whew!
Finding intercepts from a table is a lot harder than finding them from a graph or an equation,
but practice makes perfect.
In the next lesson, we'll use our knowledge of slope at intercepts to compare word problems
with graphs.