Finding X- and Y-Intercepts


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Posted by markmorse@nocharge.com (66.109.194.217) on October 03, 2003 at 20:40:32:

In Reply to: Graphing help! posted by on October 03, 2003 at 16:54:56:


I'm going to paste part of a response about intercepts from another post. Read through it, and then I'll talk about graphing your equation.

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When graphing a line by plotting points, two easy points to choose are the intercepts. The x-intercept is the point where the line crosses the x-axis. Likewise, the y-intercept is the point where the line crosses the y-axis.

They're easy because we memorize the following:

The y-coordinate of the x-intercept is always zero. In other words, it takes this form:

(x,0)

The x-coordinate of the y-intercept is always zero. In other words, it takes this form:

(0,y)

This should make sense because it's those zeros that cause the points to fall on the axes.

Now we need to calculate the x- and y-intercepts using the equation of the line given in problem 1.

x + 2y = 8

We'll find the x-intercept first. Remember, it looks like (x,0). Since y equals zero in the x-intercept, we replace the y in the equation with zero.

x + 2(0) = 8

x = 8

So, the coordinates of the x-intercept are (8,0).

Next, we'll find the coordinates of the y-intercept. Remember, it looks like (0,y). Since x equals zero in the y-intercept, we replace the x in the equation with zero.

0 + 2y = 8

2y = 8

y = 4

So, the coordinates of the y-intercept are (0,4).

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Okay, I hope that example helps you to understand that finding the intercepts amounts to replacing x or y in your equation with zero and then solving for the remaining variable.

y = x^2 - 4

This is a second-degree equation, so we know that the shape of its graph is a parabola.

Let y = 0 to find the x-intercepts.

0 = x^2 - 4

Can you solve this equation for x? You should get two values because this particular parabola crosses the x-axis in two different places.

Let x = 0 to find the y-intercept.

y = 0 - 4

Can you write the coordinates of the y-intercept from this?

Let us know what part(s) about x- and y-intercepts that you don't understand.

You can find the coordinates of some other points to help you graph this parabola. Pick a number for the x-coordinate of the point. For example, let x equal one.

(1,y)

To find the value of y, we substitute 1 for x in the equation.

y = (1)^2 - 4

y = 1 - 4

y = -3

So, the parabola passes through the point (1,-3).

You can find the coordinates of as many points as you like. Just pick different values for x, and then find the y-coordinate as shown.

Let us know if you need more help graphing this equation.

~ Mark



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