Straight line graphs : answers.

1.1.1
25 tons
1.1.2
85 tons
1.2.1
60 Ha
1.2.2
80 Ha
1.3
40 Ha
1.4
100 tons
40 Ha
mass
1.5
Yes. The rate     --------------     remains constant, viz. 2 tons/Ha .
area
2.1.1
5 litres
2.1.2
14 litres
2.2.1
150km
2.2.2
420 km
2.3
7 litres/100 km
2.4
2.1.1
4,9 litres
2.1.2
14 litres
2.2.1
71,429 km
2.2.2
428,571 km
distance
170 km
340 km
595 km
3.1
Yes, the rate stays the same.    --------------    =    -------------    =    -------------    =    ---------    =    85 km/h
time
2 h
4 h
7 h
3.2
The graph will be a straight line
because the rate, as shown in 3.1,
remains constant.
3.3
85 km/h. It remains constant.
3.4
a = 3,5 h ; b = 552,5 km
3.5
See accompanying graph.
3.6.1
1,25 h
3.6.2
765 km
3.6.3
700 km
4.1
m   =   2   ; c   =   3
4.2
B (0   ;   3)   ;   A (-1,5   ;   0)
4.3
Yes.
4.4
P ( 0,5   ;   4)   ; Q (1,5   ;   6)   ; D (1,5   ;   4)
4.5
PD   = 1   ;   QD   =   2
QD            2
4.6
-------   =   ----   =   2
PD            1
4.7
Very well - this value   =   m
TV            2
4.8
-------   =   ----   =   2
SV            1
4.9
Very well - this value   =   m
5.1
m   =   -5 ;   c   =   4
FG           -1                      SQ            -2
5.2
--------   =   ----   =   -2        --------   =   ----   =   -2
DG          0,5                     PS            1
5.3
They are equal to m.
5.4
A (0   ;   3)    ;    B(1,5   ;   0).
6.
m   =   1   ;   c   =   3
7.
m   =   -1   ;   c   =   6
2
-3
8.
m   =   ---   ;   c   =   1
9.
m   =   -----   ;   c   =   2
3
4
10.
y = mx + c
11.
y = mx + c
(0   ;   -5)   : -5 = m(0) + c
(0   ;   5) : 5 = m(0) + c
-5 = c
5 = c
(2,5   ;   0)   : 0 = m(2,5) + (-5)
(2,5   ;   0) : 0 = m(2,5) + (5)
2 = m
-2 = m
y = 2x - 5
y = 5 - 2x
12.
y = mx + c
Substitute (-2 ; -10)   :       -10 = m(-2) + c
-2m + c = -10    ---- (1)
Substitute (3 ; 20)   :           20 = m(3) + c
3m + c = 20   ---- (2)
(2) - (1) :                       5m = 30      Eliminate c
m = 6
Into (2) :                               3(6) + c = 20          - - - - - Substitute m = 6 into equation 2
c = 2
y = 6x + 2
13.
y = mx + c
14.
y = mx + c
(-4:34) : 34 = m(-4) + c
(-5;-9) : -9 = m(-5) + c
-4m + c = 34    --   (1)
-5m + c = -9    --   (1)
(5;-11) : -11 = m(5) + c
(15;3) : 3 = m(15) + c
5m + c = -11    --   (2)
15m + c = 3    --   (2)
(2) - (1) :    9m = -45
(2) - (1) :    20m = 12
m = -5
m = 0,6
Into (1) :     -4(-5) + c = 34
Into (1) :     -5(0,6) + c = -9
c = 14
c = -6
y = 14 - 5x
y = 0,6x - 6
15.
y = 3x + 4
16.
y = -3x + 4

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