# Homework Help: Linear Intercepts (lol) / Completing The Square

1. May 9, 2006

### Richay

A couple more i'm having problems with.

First with linear intercepts.

Find the y-intercept of a line going through (3, 0) and having a slope of -5

y=mx+b

m = -5

And from then on, I don't know how to continue with this problem.

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Now, completing the square.

Solve: Solve: 4x^2 - x - 5 = 0

Steps:
4x^2 – x = 5

x^2 - 1/4x = 5/4

-1/4 --> 1/16

x^2 - 1/2x + 1/16 = 5/4 + 1/16

(x-1/4)^2 = 21/16

Solve for x now right? Well i think i already messed up in one of my earlier steps. I need help.

Thanks for any help...

2. May 9, 2006

### Pyrrhus

Do you know what b means in y = mx +b?? (hint: that's what you are looking for)

Check again your work for completing the square.

Last edited: May 9, 2006
3. May 9, 2006

### Richay

b is the value of the y-intercept.

4. May 9, 2006

### Curious3141

The y-intercept is the value y assumes when x = 0. This is when the line cuts through the y-axis. In the equation y = mx + b, what does y equal when x = 0 ?

You're given a point on the line which is essentially the y-value for a specific x-value. You also know the slope (m). Now put those back in and work out b.
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It's OK up to this step : x^2 - 1/4x = 5/4

In completing the square, you are basically comparing the left hand side (LHS) to (x-c)^2 = x^2 - 2cx + c^2.

Now compare the coefficient of the x term in that expansion to your own LHS and find out the value of c. The square of that expression then bears a remarkable resemblance to your original equation, and all you need to do is add constants to make it identical, then you can solve it.