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## Intercepts

# x-intercept of a line

CCSS.Math: , ,

## Video transcript

The graph of the line
2y plus 3x equals 7 is given right over here. Determine its x-intercept. The x-intercept is the x
value when y is equal to 0, or it's the x value
where our graph actually intersects the x-axis. Notice right over here
our y value is exactly 0. We're sitting on the x-axis. So let's think about what
this x value must be. Well, just trying to
eyeball a little bit, it's a little over 2. It's between 2 and 3. It looks like it's
less than 2 and 1/2. But we don't know
the exact value. So let's go turn to the equation
to figure out the exact value. We essentially
have to figure out what x value, when
y is equal to 0, will have this equation be true. So we could just say 2 times
0 plus 3x is equal to 7. Well, 2 times 0 is
just going to be 0, so we have 3x is equal to 7. Then we can divide both
sides by 3 to solve for x, and we get x is equal to 7/3. Does that look like 7/3? Well, we just have
to remind ourselves that 7/3 is the same
thing as 6/3 plus 1/3. And 6/3 is 2. So this is the same
thing as 2 and 1/3. Another way you could
think about it is 3 goes into 7 two times, and
then you have a remainder of 1. So you've still got
to divide that 1 by 3. It's 2 full times
and then a 1/3, so this looks like 2 and 1/3. And so that's its
x-intercept, 7/3. If I was doing this on the
exercise on Khan Academy, it's always a little easier to
type in the improper fraction, so I would put in 7/3.