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Equation in Slope Intercept or Point Slope Form

Date: 03/18/2002 at 13:08:13
From: Andrea
Subject: Geometry

I have not been able to find the answers to my problem, or maybe I 
have and don't know it. Here are my questions:

Question 1: Find an equation of the line with slope -4/3 and y-
intercept 3.  Leave the equation in slope intercept form. 

What do they mean by leaving it in slope intercept form?

Is it -4/3x + 3 ? 
Is it y = mx + b ?

I'm not sure if they are asking for the formula or the actual problem.

Question 2: Find an equation of the line that goes through the point 
(2.1) and has a slope of 4. Leave the equation in point slope form.

Again, I'm not sure what they are asking.

Is it 2-1 = 4(x-1), 2-1 = 4(x-x) ?
Is it Y-Y = M(x-x) ?

Question 3:  Given points C(4,3) and D(2,-5), find the slope of every 
line parallel to CD. I can't find anything in my book that shows me 
how to do this, or maybe I am overlooking it.

Question 4: Given points R(-2,3) and S(5,1), find the slope of every 
line perpendicular to RS. Again, I don't see anything that shows me 
how this is done.


Date: 03/18/2002 at 13:35:01
From: Doctor Peterson
Subject: Re: Geometry

Hi, Andrea.

You have some good questions here that force me to talk about some 
details we often forget to mention, because we get too used to 
assuming everyone knows what we mean.

When the problem says to leave the equation in slope-intercept form, 
they mean to leave it looking like

    y = __ x + __

with the blanks filled in. We say that slope-intercept form is

    y = mx + b

as a way of saying this: m and b are "parameters" that represent 
numbers, so to write the equation of a specific line, you replace them 
with the proper values. In a sense, a variable (in this case called a 
parameter) is just like a blank with a label on it, that says "put a 
number here." 

The parameters m and b are thought of as constants, so you want to 
replace them with specific values NOW. The variables x and y represent 
any point on the line, so you leave them in the equation and replace 
them with numbers only LATER, when you want to see if a specific point 
is on the line.

So your answer to the first question should be

    y = -4/3x + 3

Similarly, for point-slope form,

    y - y0 = m(x - x0)

means you should fill in the blanks in

    y - __ = __(x - __)

and your answer is

    y - 1 = 4(x - 2)

Notice that the given point (x0,y0) is (2,1), so that x0 = 2 and 
y0 = 1. We are replacing all the parameters x0, y0, and m, but leaving 
the variables x and y as unknown, so that any point (x,y) that makes 
the equation true is on the line.

For your last two questions you have to find the slope between the two 
points. Every line parallel to the line between them will have this 
same slope m; every line perpendicular to it will have slope -1/m. 
Replace "m" here with the actual slope you find.

Feel free to write back if you have more questions. There are a lot of 
important but subtle ideas here, but once you've asked enough 
questions to understand what's going on, you'll probably start 
forgetting it was ever hard.

- Doctor Peterson, The Math Forum   
Associated Topics:
High School Equations, Graphs, Translations

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