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
and
, and we know that the general form of the equation for a straight line is:
So, to determine the equation of the line passing through our two points, we need to determine values for
(the gradient of the line) and
(the
-intercept of the line). The resulting equation is
where
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:
We now have two equations, with two unknowns,
and
.
Now, to make things a bit easier to remember, substitute
[link] into
[link] :
If you are asked to calculate the equation of a line passing through two points, use:
to calculate
and then use:
to determine the equation.
For example, the equation of the straight line passing through
and
is given by first calculating
and then substituting this value into
to obtain
Then substitute
to obtain
So,
passes through
and
.
Find the equation of the straight line passing through
and
.
The equation of the straight line that passes through
and
is
.
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,
, and to be told that the line is parallel or perpendicular to another line. If the equation of the unknown line is
and the equation of the second line is
, then we know the following:
Once we have determined a value for
, we can then use the given point together with:
to determine the equation of the line.
For example, find the equation of the line that is parallel to
and that passes through
.
First we determine
, the slope of the line we are trying to find. Since the line we are looking for is parallel to
,
The equation is found by substituting
and
into:
Inclination of a line
In
[link] (a), we see that the line makes an angle
with the
-axis. This angle is known as the
inclination of the line and it is sometimes interesting to know what the value of
is.
Firstly, we note that if the gradient changes, then the value of
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
-direction to a change in the
-direction.
For example, to find the inclination of the line
, we know
Co-ordinate geometry
Find the equations of the following lines
through points
and
through points
and
parallel to
passing through
perpendicular to
passing through
perpendicular to
passing through the origin
Find the inclination of the following lines
(Hint: if
is negative
must be in the second quadrant)
Show that the line
for any constant
is parallel to the x-axis. (Hint: Show that the inclination of this line is
.)
Show that the line
for any constant
is parallel to the y-axis. (Hint: Show that the inclination of this line is
.)
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?