#### Straight line graphs. 1.
The accompanying diagram shows the
graph of the distance travelled by
by each of two cars, A and B.
1.1
Describe the motion of car A
for the first 2 hours, i.e. from t = 0 to t = 2
1.2
What happens at point P?
1.3
At what speed does car A travel
for the first 2 hours?
1.4
Which car travels at the higher speed
from t = 0 to t = 2? Explain.
1.5
At what average speed does car A travel from t = 0 to t = 3 hours? Explain.
1.6
At what average speed does car B travel from t = 0 to t = 3 hours?
1.7
Is there a a time when the cars travel at the same speed? Explain.
1.8
Both cars travel at the same average speed for the journey, i.e. from t = 0 to t = 6 hours.
Do you agree? Explain. 2.
The accompanying diagram shows the graph
of f:   y = 2x + 3 .
2.1
Calculate the value of y if x = –2 and x = 8.
2.2
Calculate the value of x if y = 4 and if y = –5
g is a second line defined by y = 18 – 0,5x
2.3
Calculate the value of y on g if x = –2 and if x = 8.
2.4
Calculate the value of x on g if y = 17 and if y = 13.
2.5
Calculate the co-ordinates of P, the point of
intersection of f and g.
2.6
Say which of the following statements is true and give a reason:
If x = –2 then (a) 2x + 3 = 18 – 0,5x   OR   (b) 2x + 3 < 18 – 0,5x   OR   (c) 2x + 3 > 18 – 0,5x
2.7
Say which one of the following statements is true and give a reason:
If x = –2 then (a) f = g   OR  (b) f < g   OR   (c) f > g .
2.7
Repeat 2.6 but with x = 8.
2.8
Say for which value(s) of x will (a) f < g   (b) f = g   (c) f > g
2.9
M(–2 ; –1) is a point on f and N(–2 ; 19) is a point on g. Write down the length of line MN.
2.10
Now write down the value of f – g if x = –2.
2.11
Calculate the value of f – g if x = 8   ;   x = 0,5 and x = –4,5.
2.12
For which value(s) of x will f = 0   ;   f < 0   ;   f > 0
2.13
For which value(s) of x will f.g < 0   OR   f.g = 0   OR   f.g > 0 3.
The diagram shows the graph, f, of the income
realized by selling n items and the
graph, g, of the cost to manufacture the n items.
The graphs f and g intersect at P.
3.1
Why does the line f start in the origin (0 ; 0)?
3.2
The graph of g does not start in the origin.
Explain.
3.3
When is a profit made? Use the graphs f and g
3.4
Read from the graph the income made from the sale of 4 items.
3.5
Show that the gradient of the line f is 1,5.
3.6
The graph of f passes through the origin (0 ; 0). Write down the equation of the line f.
3.7
The equation of line g is y = 0,875x + 5. Show that P, the point of intersection of f and g,
is the point (8 ; 12).
3.8