please help on my analytic geometry

**^_^Engineer_Adam^_^** · November 25th 2006, 01:00 AM

write the equation of the line which passes through the point A with the slope $m$ :

$1.)A(0,0), m = \frac {2}{7}$
$2.)A(0,3), m = 0$

thank you very much for the help...

**earboth** · November 25th 2006, 01:12 AM

Originally Posted by ^_^Engineer_Adam^_^

write the equation of the line which passes through the point A with the slope $m$ :

$1.)A(0,0), m = \frac {2}{7}$
$2.)A(0,3), m = 0$
...

Hello,

the quation of a line passing through a point $P(x_1, y_1)$ will be described by the equation:
$\frac{y-y_1}{x-x_1}=m$ (point-slope-formula of a line)

to 1: $\frac{y-0}{x-0}=\frac {2}{7}$ . Solve for y:
$y=\frac {2}{7}x$

to 2.) $\frac{y-3}{x-0}=0$
$y=3$

EB

**^_^Engineer_Adam^_^** · November 25th 2006, 01:14 AM

I see

thanks alot!

**CaptainBlack** · November 25th 2006, 01:15 AM

Originally Posted by ^_^Engineer_Adam^_^

write the equation of the line which passes through the point A with the slope $m$ :

$1.)A(0,0), m = \frac {2}{7}$
$2.)A(0,3), m = 0$

thank you very much for the help...

The equation of a line is of the form: $y=mx+c$ , where if $x=0, y=c$ .

So for 1.) $c=0$ , and we are given $m$ so the required equation is:

$<br /> y=\frac{2}{7}x<br />$

Similarly for 2.), $c=3$ and $m=0$ so:

$<br /> y=3<br />$

RonL

**Soroban** · November 25th 2006, 06:58 AM

Hello, ^_^Engineer_Adam^_^!!

There is only one formula to learn . . . Forget the others! **

Point-Slope Formula
Given a point $P(x_1,y_1)$ and the slope $m$
. . the line through point $P$ with slope $m$ is:
. . . . . $y - y_1\:=\:m(x-x_1)$

Write the equation of the line which passes through the point $A$ with the slope $m$ :

$1)\;A(0,0),\;m = \frac {2}{7}$

$y - 0 \:=\:\frac{2}{7}(x - 0)\quad\Rightarrow\quad y \:=\:\frac{2}{7}x$

$2)\;A(0,3),\;m = 0$

$y - 3 \:=\:0(x - 0)\quad\Rightarrow\quad y\:=\:3$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

** [rant]

These two problems can be solved easily with the form: $y \:=\:mx + b$
But I find the alternate forms unnecessary/confusing/annoying.

Did you know that some textbooks teach you four formulas?

$(1)\;y - y_1\:=\:m(x-x_1)$ . . . in case you're given the slope and any point

$(2)\;y \:=\:mx + b$ . . . in case you're given the slope and the y-intercept

$(3)\;y-y_1 \:=\:\frac{y_2-y_1}{x_2-x_1}(x-x_1)$ . . . in case you're given two points

$(4)\;\frac{x}{a} + \frac{y}{b} \:=\:1$ . . . in case you're given the two intercepts

(2) is unnecessary because the y-intercept is simply a point $(0,b)$
. . .and we can use formula (1).

(3) is unnecessary because, given two points, we can find the slope
. . .with the formula: $m \,=\,\frac{y_2-y_1}{x_2-x_1}$ ... and we can use formula (1).

(4) is unnecessary because we are given two points $(a,0)$ and $(0,b)$
. . . The slope is: $m = \frac{b-0}{0-a} = -\frac{b}{a}$ ... and we can use formula (1).

[/rant]

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