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

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

$\displaystyle 2.)A(0,3), m = 0$

thank you very much for the help...:)

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- Nov 25th 2006, 01:00 AM^_^Engineer_Adam^_^please help on my analytic geometry
write the equation of the line which passes through the point A with the slope $\displaystyle m$:

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

$\displaystyle 2.)A(0,3), m = 0$

thank you very much for the help...:) - Nov 25th 2006, 01:12 AMearboth

Hello,

the quation of a line passing through a point $\displaystyle P(x_1, y_1)$ will be described by the equation:

$\displaystyle \frac{y-y_1}{x-x_1}=m$ (point-slope-formula of a line)

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

$\displaystyle y=\frac {2}{7}x$

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

$\displaystyle y=3$

EB - Nov 25th 2006, 01:14 AM^_^Engineer_Adam^_^
I see

thanks alot! - Nov 25th 2006, 01:15 AMCaptainBlack
The equation of a line is of the form: $\displaystyle y=mx+c$, where if $\displaystyle x=0, y=c$.

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

$\displaystyle

y=\frac{2}{7}x

$

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

$\displaystyle

y=3

$

RonL - Nov 25th 2006, 06:58 AMSoroban
Hello, ^_^Engineer_Adam^_^!!

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

**Point-Slope Formula**

Given a point $\displaystyle P(x_1,y_1)$ and the slope $\displaystyle m$

. . the line through point $\displaystyle P$ with slope $\displaystyle m$ is:

. . . . . $\displaystyle y - y_1\:=\:m(x-x_1)$

Quote:

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

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

Quote:

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

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

******[rant]

These two problems can be solved easily with the form: $\displaystyle y \:=\:mx + b$

But I find the alternate forms unnecessary/confusing/annoying.

Did you know that some textbooks teach you**four**formulas?

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

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

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

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

(2) is unnecessary because the y-intercept is simply a point $\displaystyle (0,b)$

. . .and we can use formula (1).

(3) is unnecessary because, given two points, we can find the slope

. . .with the formula: $\displaystyle m \,=\,\frac{y_2-y_1}{x_2-x_1}$ ... and we can use formula (1).

(4) is unnecessary because we are given two points $\displaystyle (a,0)$ and $\displaystyle (0,b)$

. . . The slope is: $\displaystyle m = \frac{b-0}{0-a} = -\frac{b}{a}$ ... and we can use formula (1).

[/rant]