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...
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
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
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:
. . . . . $\displaystyle y - y_1\:=\:m(x-x_1)$
$\displaystyle y - 0 \:=\:\frac{2}{7}(x - 0)\quad\Rightarrow\quad y \:=\:\frac{2}{7}x$Write the equation of the line which passes through the point $\displaystyle A$ with the slope $\displaystyle m$:
$\displaystyle 1)\;A(0,0),\;m = \frac {2}{7}$
$\displaystyle y - 3 \:=\:0(x - 0)\quad\Rightarrow\quad y\:=\:3$$\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]