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standard-form linear eqn for line through (7, 4) and (7, 3)
- Thread starter acelethal
- Start date
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Deleted member 4993
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Re: linear equations
First of all, the general form of a straight line is:
\(\displaystyle Ax \, + \, By \, = \, C\) ............ where A, B and C are integers
or
\(\displaystyle \frac{A}{C}x \, + \, \frac{B}{C}y \, = \, 1\)
or
\(\displaystyle Mx \, + \, Ny \, = \, 1\)
Here we need to solve for M & N . In general M and N will be fractions. For general equation, you will need to convert those to integers.
Given twopoints (x[sub:1mazw415]1[/sub:1mazw415], y[sub:1mazw415]1[/sub:1mazw415]) and (x[sub:1mazw415]2[/sub:1mazw415], y[sub:1mazw415]2[/sub:1mazw415]), you get two equations with two unknowns as follows:
\(\displaystyle Mx_1 \, + \, Ny_1 \, = \, 1\)
and
\(\displaystyle Mx_2 \, + \, Ny_2 \, = \, 1\)
This is a linear system of equations - 2 equations and 2 unknowns (M & N). If you need to review - how to solve such equations - go to:
http://www.purplemath.com/modules/systlin4.htm
and brush up.
But before doing anything - get a sheet of paper and plot those two points - and join those.
You'll see this is a special type of line, and all the calculations shown above may be unnecessary (however, it is correct). You should be able to look at the line - and know its equation. But since you said you have been out of math for a while - so numerical exercize along with graphical confirmation will be good for you.
I'll do a general problem for you.acelethal said:I have not done this type of algebra in ages and i'm a little rusty... any help would be appreciated...
Find the standard form of the equation of the line.
the points given are : (7,4) (7,3)
First of all, the general form of a straight line is:
\(\displaystyle Ax \, + \, By \, = \, C\) ............ where A, B and C are integers
or
\(\displaystyle \frac{A}{C}x \, + \, \frac{B}{C}y \, = \, 1\)
or
\(\displaystyle Mx \, + \, Ny \, = \, 1\)
Here we need to solve for M & N . In general M and N will be fractions. For general equation, you will need to convert those to integers.
Given twopoints (x[sub:1mazw415]1[/sub:1mazw415], y[sub:1mazw415]1[/sub:1mazw415]) and (x[sub:1mazw415]2[/sub:1mazw415], y[sub:1mazw415]2[/sub:1mazw415]), you get two equations with two unknowns as follows:
\(\displaystyle Mx_1 \, + \, Ny_1 \, = \, 1\)
and
\(\displaystyle Mx_2 \, + \, Ny_2 \, = \, 1\)
This is a linear system of equations - 2 equations and 2 unknowns (M & N). If you need to review - how to solve such equations - go to:
http://www.purplemath.com/modules/systlin4.htm
and brush up.
But before doing anything - get a sheet of paper and plot those two points - and join those.
You'll see this is a special type of line, and all the calculations shown above may be unnecessary (however, it is correct). You should be able to look at the line - and know its equation. But since you said you have been out of math for a while - so numerical exercize along with graphical confirmation will be good for you.