







For those of you who watch or play football, then you are familiar with the term 'interception.' For those of you who aren't, well, stop and think for just a second what interception just might mean…
Why all this talk about football? Isn't this a website about math? Yeah, sure but let's take a look at football for a second and then make the connection to math, shall we?







In a linear equation, y = mx + b,
 a point where the line crosses the yaxis
 it is the number when x is zero (0)
 is represented by the letter b in the linear equation y = mx + b










In football, a quarterback (offensive player) for team A throws a pass. Unfortunately, a defensive player from team B intercepts the ball before someone from team A can catch it.






Team B is thrilled! They have thwarted the other team! Bummer for Team A…
So, how does all of this relate to math and linear equations?




Pretend that the quarterback is throwing the ball and the path it is taking is the line.
Here is a picture to help you 'get' it. We always read from lefttoright so the quarterback is on the left. He throws the ball to the right so the ball is going UP. Let's see what happens.





Team B (the yaxis) intercepts the pass. In this picture, the point of interception is circled.
This means that the point where the line crosses the yaxis is the point of interception or the yintercept.
The point the line crossed is at (0, 2).
In the linear equation formula, y = mx + b, think of the b as ball.
In a coordinate pair your numbers are set up (x, y). If we are looking for the 'y' for our ball for the yintercept, which one would it be from our point? Did you say 2? Hooray!
Just substitute THAT number in the equation!
 y = mx + 2












Cool! Now that you understand the vocabulary from a football pointofview and you know the definition of what a yintercept is, let's see how you can find the yintercept from looking at a graph.







Step 1: Look at the line. Find where it crosses the yaxis.








Step 2: Draw a CIRCLE around the point where the line crosses the yaxis.








Step 3: Write down the basic linear equation form y = mx + b.
Substitute the number you circled for the b.









Step 4: Go find the slope to finish your equation! y = mx + b.







So, after all this yintercept talk, what about the xintercept? Huh?
Here's the deal…you have been working with the xintercept but just didn't know it. The xintercept is the point where the line crosses the xaxis. (Duh!) Think about it…the yintercept is the point where a line crosses the yaxis, right? So, doesn't it make sense that the xintercept is the point where the line crosses the xaxis? See? It isn't anything new.
The BIG question now isn't going to be finding it on the graph but how do you find it if you have an EQUATION like this:








How do you find both the y and xintercept in an equation like this?
This isn't as hard as it may seem. Check it out.




Step 1: Substitute ZERO for each variable.
 To find the xintercept, substitute the y with a 0.
 To find the yintercept, substitute the x with a 0.







Step 2: Solve for the variable in the equation.
 The equation on the left side gives you the yintercept!
 The equation on the right side gives you the xintercept!







That's it! Voila!
Easypeasy, lemonsqueasy!






©2011–2017 Sherry Skipper Spurgeon.
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