Finding the equation of a straight line graph from a diagram
ACTIVITY 1
To find the equation of a straight line graph from a diagram
[LO 2.5]
If we can find out the values of
m and
c , then we simply substitute them in the general equation
y =
mc +
c to give us the defining equation of the line. Let’s do an example from the given diagram.
To find c is easy as it is the value (positive or negative or zero) where the line cuts the y–axis. Substitute this value (it is –1) for c.
The equation now becomes y = mx – 1. To find the gradient (the value of m) we construct the right-angled triangle between two suitable points where the graph goes exactly through corners on the graph paper.
Remembering that m is a fraction:
change in vertical distance
change in horizontal distance
We read off the number of units of the height and the length of the triangle to give us the numerator and denominator respectively
We also have to decide whether the sign is negative or positive by looking at which way the line slopes.
This gives us:
(remember to simplify the fraction).
This value is now substituted for m in the equation:
. This gives us the defining equation of the line in the diagram.
Going back to the previous section, use this method to find the defining equations of the eight graphs in the first two diagrams.
2 How do we deal with horizontal and vertical graphs? They are the easiest.
If the line is horizontal, then the equation is
y =
c . We have to replace the
c by a value. We read this value off the graph – it is the
y –intercept! Substitute this into
y =
c , and you have the defining equation.
If the line is vertical, the equation is
x =
k . Find
k by reading from the graph where the line cuts the
x –axis and substitute this number for
k . This gives the defining equation.
From the previous section, find the equations for the four graphs in the last diagram.
Here are the answers:
y = 1 and
y = –1,5 are the two horizontal lines, and
x = –1 and
x = –2,5 are the two vertical lines.
3 The following diagrams have a mixture of lines for you to test your skills on.
4 Did you notice that the gradients (
m ) of lines G and H are the same? Why is this?
ACTIVITY 2
To calculate the gradient of a straight line from two points on the line
[LO 2.5]
If you know the coordinates of two points on a certain straight line, then you can draw that line, as you have seen. And from the sketch you can find the gradient as you have already learnt. But it is not necessary to have a graph to find the gradient.
Here is an example: The points (3 ; –1) and (4 ; 2) are on a certain straight line.
First we calculate the vertical distance between the two points by subtracting the second point’s
y -coordinate from the first point’s
y –coordinate. This is the numerator of the gradient.
Then we calculate the horizontal distance between the two points by subtracting the second point’s
x -coordinate from the first point’s
x -coordinate. This is the denominator of the gradient.
So, the gradient 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?
