General 3 Straight line graphs

1
General 3 Straight line graphs

• Breithaupt chapter 16.4
• pages 238 and 239

2
The equation of a straight line graph

• For any straight line
• y mx c
• where
• m gradient
• (yP yR) / (xR xQ)
• and
• c y-intercept

3
Direct proportion

• Physical quantities are directly proportional to
  each other if when one of them is multiplied by a
  certain factor the other changes by the same
  amount.
• For example if the extension, ?L in a wire is
  doubled so is the tension, T
• A graph of two quantities that are proportional
  to each will be
• a straight line
• AND passes through the origin
• The general equation of the straight line in this
  case is y mx, with, c 0

4
Linear relationships - 1

• Physical quantities are linearly related to each
  other if when one of them is plotted on a graph
  against the other, the graph is a straight line.
• In the case opposite, the velocity, v of the body
  is linearly related to time, t. The velocity is
  NOT proportional to the time as the graph line
  does not pass through the origin.
• The quanties are related by the equation v u
  at. When rearranged this becomes v at u.
• This has form y mx c
• In this case m gradient a
• c y-intercept u

5
Linear relationships - 2

• The potential difference, V of a power supply is
  linearly related to the current, I drawn from the
  supply.
• The equation relating these quantities is V e
  r I
• This has the form y mx c
• In this case
• m gradient - r (cell resistance)
• c y-intercept e (emf)

6
Linear relationships - 3

• The equation relating these quantities is EKmax
  hf f
• This has the form y mx c
• In this case
• m gradient h (Planck constant)
• c y-intercept f (work function)
• The x-intercept occurs when y 0
• At this point, y mx c becomes
• 0 mx c
• x x-intercept - c / m
• In the above case, the x-intercept, when EKmax
  0
• is f / h

The maximum kinetic energy, EKmax, of electrons
emitted from a metal by photoelectric emission is
linearly related to the frequency, f of incoming
electromagnetic radiation.
7
Calculating the y-intercept

• The graph opposite shows two quantities that are
  linearly related but it does not show the
  y-intercept.
• To calculate this intercept
• 1. Measure the gradient, m
• In this case, m 1.5
• 2. Choose an x-y co-ordinate from any point on
  the straight line. e.g. (12, 16)
• 3. Substitute these into y mx c, with (P y
  and Q x)
• In this case 16 (1.5 x 12) c
• 16 18 c
• c 16 - 18
• c y-intercept - 2

8
Questions

• Quantity P is related to quantity Q by the
  equation P 5Q 7. If a graph of P
  against Q was plotted what would be the gradient
  and y-intercept?
• Quantity J is related to quantity K by the
  equation J - 6 K/3. If a graph of J
  against K was plotted what would be the gradient
  and y-intercept?
• Quantity W is related to quantity V by the
  equation V 4W 3. If a graph of W against
  V was plotted what would be the gradient and
  x-intercept?

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Answers

• Quantity P is related to quantity Q by the
  equation P 5Q 7. If a graph of P
  against Q was plotted what would be the gradient
  and y-intercept?
• Quantity J is related to quantity K by the
  equation J - 6 K/3. If a graph of J
  against K was plotted what would be the gradient
  and y-intercept?
• Quantity W is related to quantity V by the
  equation V 4W 3. If a graph of W against
  V was plotted what would be the gradient and
  x-intercept?

m 5 c 7
m 0.33 c 6
m - 0.25 x-intercept 3 (c 0.75)
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Notes from Breithaupt pages 238 239

• Copy figure 2 on page 238 and define the terms of
  the equation of a straight line graph.
• Copy figure 1 on page 238 and explain how it
  shows the direct proportionality relationship
  between the two quantities.
• Draw figures 3, 4 5 and explain how these
  graphs relate to the equation y mx c.
• How can straight line graphs be used to solve
  simultaneous equations?
• Try the summary questions on page 239

11
Answers to the summary questions on page 239