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# Worked example: intercepts from an equation

CCSS.Math:

## Video transcript

we're told to find the x and y-intercepts for the graph of this equation 2y plus 1/3 X is equal to 12 and just as a bit of a refresher the x-intercept 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 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 for the x intercept when Y is equal to 0 let's solve this so we get 2 times 0 plus 1/3 X is equal to 12 I just said Y is equal to 0 right there right up at 0 for y well 2 anything times 0 is just 0 so you're just left with 1/3 X is equal to 12 to solve for x we can multiply covey the dividing both sides by 1/3 or we can multiply both sides by the reciprocal of 1/3 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 or 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 y-intercept is when X is equal to 0 and Y is equal to 6 so let's plot these two points on a 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 it might be way 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 and the point 0 6 is going to be right about 0 6 might be about right about there so that's the point 0 6 and the line will look like something like this the line will look something like that try 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