#### Straight line graphs.

1.1
Car A moves at a constant speed .
1.2
At point P car A stops and is in rest (does not move) for 1 hour, from t = 2 to t = 3.
1.3
Speed of car A = 75 km/h.
1.4
Car B travels at the higher speed because the gradient of the graph for car B is greater than
the gradient of the graph for car A.
distance
150 km
1.5
Average speed of car A   =   —————   =   ————   =   50 km/h
time
3 h
1.6
Average speed of car B   =   100 km/h.
1.7
Yes, from t = 5 to t = 6 both cars travel 100 km in 1 hour, their speed is 100 km/h.
1.8
Yes. Both cars travel 400 km in 6 ours. Their average speed = 66,667 km/h.
2.1
If x = – 2, y = –1 and if x = 8, y = 19.
The points (–2 ; –1) and (8 ; 19) are points on the line f.
We can now say that if x = –2 then y f   = –1 and if x = 8 then y f   = 19.
2.2
If y = 4 , x = 0,5 and if y = –5, x = –4.
2.3
If x = –2, y = 19 and if x = 8, y = 14.
2.4
If y = 13, x = 10 and if y = 17, x = 2.
2.5
P is the point (6 ; 15)
2.6
If x = –2 then y f   = 2x + 3 = –1 and y g   = 18 – 0,5x = 19. Therefore, if x = –2
(a)   false:   2x + 3 ≠ 18 – 0,5x   because   –1 ≠ 19 ;   –1 < 19
(b)   true;   2x + 3 < 18 – 0,5x   because   –1 < 19
(c)   false;   2x + 3 < 18 – 0,5x   because   –1 < 19
2.7
(a)   false:   f ≠ g   because   –1 ≠ 19 ;   –1 < 19
(b)   true;   f < g   because   –1 < 19
(c)   false;   f < g   because   –1 < 19
2.8
(a)   f < g   if x < 6
(a)   f = g   if x = 6
(a)   f > g   if x > 6
2.9
MN = 20
2.10
If x = –2 then f – g = 20    [Note: distance is ALWAYS POSITIVE].
2.11
If x = 8 then f – g = 19 – 14 = 5    : if x = 0,5 then f – g = – 13,75
If x = –4,5 then f – g   =   – 26,25
2.12
f = 0 if x = – 1,5   ;   f < 0 if x   < – 1,5   ;   f > 0 if x   > – 1,5
2.13
f.g < 0 if x < – 1,5    ;   f.g = 0 if x = –1,5   and f.g > 0 if x > – 1,5
3.1
There is no income from the sale of 0 items.
3.2
There may be costs involved in the production process, e.g. hiring staff, buildings, machinery, etc.
3.3
A profit is made if the income is greater than the expenses or costs.
Using the graph we want that part of the graph where the graph of the income has a greater
y value than the graph of the costs, we say that the graph of the income must be greater or
lie "above" the graph of the costs. Therefore, a profit is made if f > g.
A profit is thus made if the number of items sold is greater than the number of items at the
point of intersection of f and g.
3.4
Income = R6
Δ y             6            3
3.5
m   =   ———  =  ——  =  ——  = 1,5
Δ x             4            2
3.6
y = 1,5x
3.7
At point P   f = g, i.e. the graphs have the same y value for a certain x value, i.e. at P   y f   =   y g
f is defined by y = 1,5x and g by y = 0,875x + 5
Therefore, at P :    1,5x = 0,875x + 5
0,625x = 5
x = 8
Put x = 8 into y = 1,5x : y = 1,5 × 8 = 12
P is the point (8 ; 12)
3.8.1
No. It is the break even point. The income is equal to the costs. No profit is made and