Associated Topics || Dr. Math Home || Search Dr. Math

### Equations for Lines

```
Date: 5/29/96 at 16:19:0
Subject: Algebra Wordproblem

Dear Dr. Math,

My brother is taking a correspondence course in Algebra 2 and there
are a couple of word problems we can't figure out. I have tried
helping him but word problems I cannot do!

1. Write an equation, in standard form, of the line containing the
point P(1,-3) that is parallel to the line whose equation is 2x-y=3.

2.  Write an equation, in standard form, of the line containing
Q(-5,4) that is perpendicular to the line whose equation is 3x-2y=8.
```

```
Date: 5/30/96 at 14:19:6
From: Doctor Darren
Subject: Re: Algebra Wordproblem

1. We know that this line can also be written in the form y=2x-3, so
it and all lines parallel to it have slope = 2.  We now have a point
on our line and its slope, so we can write the line in point-slope
form as:

(y-(-3)) = 2(x-1)
y+3 = 2x-2
2x-y = 5

2. The line 3x-2y=8 has slope equal to 3/2.  We know that if two lines
are perpendicular then their slopes are negative reciprocals of each
other (i.e. if a line has slope m, all lines perpendicular to it have
slope -1/m). So the slope of the line that we want is -2/3. As in the
previous problem, we now have the slope of the line and a point on the
line.  Therefore, the line can be written in point-slope form as:

y-4 = (-2/3)(x-(-5))
y-4 = (-2/3)x - 10/3
3y-12 = -2x-10
3y+2x = 2

I hope this helps!

-Doctor Darren,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search