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.
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
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what is differents between GO and RGO?
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what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
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brayan
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