There are many different methods of specifying the requirements for determining the equation of a straight line. One option is to find the equation of a straight line, when two points are given.
Assume that the two points are
$({x}_{1};{y}_{1})$ and
$({x}_{2};{y}_{2})$ , and we know that the general form of the equation for a straight line is:
$$y=mx+c$$
So, to determine the equation of the line passing through our two points, we need to determine values for
$m$ (the gradient of the line) and
$c$ (the
$y$ -intercept of the line). The resulting equation is
$$y-{y}_{1}=m(x-{x}_{1})$$
where
$({x}_{1};{y}_{1})$ are the co-ordinates of either given point.
Finding the second equation for a straight line
This is an example of a set of simultaneous equations, because we can write:
The equation of the straight line that passes through
$(-3;2)$ and
$(5;8)$ is
$y=\frac{3}{4}x+\frac{17}{4}$ .
Equation of a line through one point and parallel or perpendicular to another line
Another method of determining the equation of a straight-line is to be given one point,
$({x}_{1};{y}_{1})$ , and to be told that the line is parallel or perpendicular to another line. If the equation of the unknown line is
$y=mx+c$ and the equation of the second line is
$y={m}_{0}x+{c}_{0}$ , then we know the following:
In
[link] (a), we see that the line makes an angle
$\theta $ with the
$x$ -axis. This angle is known as the
inclination of the line and it is sometimes interesting to know what the value of
$\theta $ is.
Firstly, we note that if the gradient changes, then the value of
$\theta $ changes (
[link] (b)), so we suspect that the inclination of a line is related to the gradient. We know that the gradient is a ratio of a change in the
$y$ -direction to a change in the
$x$ -direction.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?