If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

### Course: MAP Recommended Practice>Unit 19

Lesson 15: Intercepts

# Worked example: intercepts from an equation

Let's find the x- and y-intercepts of the equation 2y + 1/3x = 12, where a line crosses the x-axis (the x-intercept) and the y-axis (the y-intercept) on a graph. To find the x-intercept, we make y equal to 0 and solve the equation for x. To find the y-intercept, we make x equal to 0 and solve for y. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• I know in the equation y=mx+b, b is the y-intercept. Is there a x-intercept in another slope equation? Thanks!
(7 votes)
• Slope intercept form is y=mx+b. Really, it is more like "Rise/Run Slope of a line from the y-intercept form". If you want to know the x-intercept form you can solve the equation for x.

y=2x+4 would become x=1/2y-2. Now plug in zero for y and you will have what x is equal to (-2). The reason we use y=mx+b is because the idea of rise/run no longer works correctly in this version of slope x-intercept. You have run/rise instead of rise/run. This is unwanted confusion as now you have

y=mx+b "Rise/Run Slope of a line from the y-intercept form"
and
x=my+b "Run/Rise Slope of a line from the x-intercept form"

I hope this helped you find the x-intercept and also why we only use y-intercept slope formulas.
(9 votes)
• How do you find intercepts when the formula is more complex as in y=x*sqrt(16-x^2)
(7 votes)
• The general rule of thumb for finding intercepts is to plug 0 in for the other number. To finish the equation you provided, you would need to use the zero-product property to set each piece equal to zero and solve..
(6 votes)
• Need help, what do the "|" mean in an equation? Example, y=|x-2|
Thanks
(6 votes)
• those are called absolute value bars, no matter what is inside the absolute value bars, it comes out as positive. So, for example |4| = 4 and |-4| = 4.
(7 votes)
• So, if you wanted to do the same (figure out the x and y intercept) for any other equation, should I only use 0 as a substitute to figure them out? Would it be the same if you used other numbers as substitutes?
(6 votes)
• Katie, yes, exactly. If the equation is in standard form:ax+by=c then you just set x equal to 0 to find the y intercept and set y equal to 0 to find the x intercept. It makes sense, right. The y intercept is when the line crosses the y axis, so x will always be 0, so that is why we set x equal to 0. To find where the line crosses the y axis.

The same logic applies when finding the x intercept, set y equal to 0 to find where the line crosses the x axis, because y will always be zero at the x intercept.
Ex: (0,8) y intercept, notice x is 0
(2,0) x intercept notice y is 0
(7 votes)
• Is there a rule governing linear coordinates that pass the exact centre of the graph?
For instance, where Xintercept=Yintercept=0...

Since you can't draw a linear graph from using just one point, what can we do with such information?
I understand a lot of formulas will meet with the centre, and the lines can angle 360degrees,
through all quadrants of the graph when it does.
But is it some type of typical linear graph? Or is there special methods involved?
What can we know about situations that don't work while originally meeting the demands for the X/Yintercept method? (crossing both x0 and y0, being a linear equation etc.)
Perhaps it is a singular exception?

Sorry for this weakly translated and confusing question.
I'd like to hear anything people got to say about this.
(6 votes)
• When linear coordinates pass the exact centre of the graph, i.e. x-int=y=int=0; you cannot draw a line just based off this information due to the fact that it is quintessential that you have or know a minimum of 2 points in order to graph the line. Factors of a line which will help in this scenario will include; the gradient, the equation of the line and even just simple another point. Hope this helps!
(5 votes)
• How do answer questions about slope in word problems? That is my problem on math test with any unit.
(7 votes)
• (1 vote)
• These videos make me tired.
(5 votes)
• Can X and Y be negative
(3 votes)
• Simple answer, Yes
(2 votes)
• Hello guys
May I have some further explanation of figuring intercepts from charts and equations?
Thank you
(3 votes)
• What if you have 2 points and you have to find the slope, y intercept, and x intercept then put it into an equation?
(2 votes)

## Video transcript

We're told to find the x- and y-intercepts for the graph of this equation: 2 y plus 1/3x is equal to 12. And just as a bit of a refresher, the x-intercept is the point on the graph that intersects the x-axis. So we're not above or below the x-axis, so our y value must be equal to 0. And by the exact same argument, the y-intercept occurs when we're not to the right or the left of the y-axis, so that's when x is equal to 0. So let's set each of these values to 0 and then solve for what the other one has to be at that point. So for the x-intercept, when y is equal to 0, let's solve this. So we get 2 times 0, plus 1/3x is equal to 12. I just set y is equal to 0 right there, right? I put 0 for y. Well, anything times 0 is just 0, so you're just left with 1/3x is equal to 12. To solve for x, you can think of it as either dividing both sides by 1/3, or we can multiply both sides by the reciprocal of 1/3. And the reciprocal of 1/3 is 3, or you can even think of it as 3 over 1. So times 3 over 1. And so we're left with 3 times 1/3, that just cancels out, so you're left with x is equal to 12 times 3, or x is equal to 36. So when y is equal to 0, x is 36. So the point 36 comma 0 is on the graph of this equation. And this is also the x-intercept. Now, let's do the same thing for the y-intercept. So let's set x equal 0, so you get 2y plus 1/3, times 0 is equal to 12. Once again, anything times 0 is 0. So that's 0, and you're just left with 2y is equal to 12. Divide both sides by 2 to solve for y, and you're left with y is equal to 12 over 2, is 6. So the y-intercept is when x is equal to 0 and y is equal to 6. So let's plot these two points. I'll just do a little hand-drawn graph, and make it clear what the x- and the y-intercepts are. So let me draw-- that's my vertical axis, and that is my horizontal axis-- and we have the point 36 comma 0. So this is the origin right here, that's the x-axis, that's the y-axis. The point 36 comma 0 might be all the way over here. So that's the point 36 comma 0. And if that's 36, then the point 0, 6 might be right about there. So that's the point 0, 6. And the line will look something like this. I'm trying my best to draw a straight line. And notice where the line intercepted or intersected the y-axis, that's the y-intercept, x is 0, because we're not to the right or the left of it. Where the line intersected the x-axis, y is 0, because we're not above or below it.