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# finding intercept of graph of equation

how do i find the intercept of a given algebra equation

Do you have a specific problem I can use as an example?

1/23/2013

Hi, Harry.

Because you didn't state an example of how your equation looks, I will keep my answer rather generic.

The easiest way to understand intercepts is to think about where the line crosses the x-axis (x-intercept) or the y-axis (y-intercept).  If you like football, think of what occurs when there's an interception.  A player from the defense crosses over the imaginary line between the quarterback and the intended receiver to catch the football.  Where the player crosses that line is the location of the interception.

Back to Algebra - to calculate an intercept, make the "other variable" have the value of zero.  For example, to find the x-intercept, set y = 0, and solve the new equation.  Your answer should be (something, zero) for an x-intercept.  Similarly, to find the y-intercept, set x = 0, and solve the new equation.  Your answer should be (zero, something).

Sample problem:  3x + 2y = 6

If we let y = 0, then our new problem will be 3x + 2(0) = 6
Solving this:
3x + 0 =6
3x = 6
x = 2
So, the x-intercept is (2, 0)

If we let x = 0, then our new problem will be 3(0) + 2y = 6
Solving this:
0 + 2y = 6
2y = 6
y = 3
So, the y-intercept is (0, 3)

Hope this helps you.

Since you didn't indicate which, I'll answer the question for both x-intercept and y-intercept.

Assuming that you already have an equation if the following form, finding the y-intercept is easy:
y = mx + b

In this case, b is the y-intercept.

Remember that, in order for a point on a graph to be a y-intercept, the point must rest on the y-axis, and the ONLY way that can be is if the point's x-coordinate is 0.

Since we can assume that x = 0, the above equation becomes the following:

y = m(0) + b

Since we are now multiplying by 0, we can eliminate m(0) from the equation, since it can only be 0.

y = b, therefore b is the y-intercept.

The x-intercept is the trickier of the two, but not by much. In this case, instead of assuming x = 0, we must assume y = 0. (In other words, an x-intercept requires that our y-coordinate be 0, so it can appear in the x-axis).

0 = mx + b

In this case, we need to get x by itself in order to determine where on the x-axis the x-intercept appears. This requires two steps:

1. subtract the y-intercept (b) from both sides
2. divide the slope (m) from both sides

Example:

0 = mx + b

0 - b = mx + b - b

-b = mx (since 0 minus anything is its inverse, and anything minus itself is 0)

-b / m = mx / m

-b / m = x (since anything divided by itself is 1).

Therefore, the x-intercept is the inverse of the y-intercept divided by the slope.

In short, given y = mx + b...

• The y-intercept is b.
• The x-intercept is -b/m.

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