Grade 11 - More exercises.
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
