Page 143 - Mathematics

(a) Represent the above information as points in the xy-plane and draw
a line through the points.

(b) Determine;
(i) The gradient of the line and state what it signifies
(ii) The equation of the line and x and y-intercepts
(c) Using the equation of the line obtained in b(ii), determine; Tanzania Institute of Education
(i) The number of bags Nyanda will need for his 24 acres farm
(ii) The size of the Myoma farm if she bought 75 bags of fertilizers.
8. The sewage and water authority total charges (y) include a fixed service
charge and variable charge depending on the number of units of water
consumed (x). In a certain month, Kelvin paid Tshs 70 for 10 units and
in another month he paid Tshs 95 for 15 units.
(a) Determine the equation representing the information and by using
a suitable scale, draw the graph of the equation.
(b) Find:

(i) the y-intercept and state what it represent
(ii) the slope of the line and state what it represent

General equation of a straight line
Equation in the form y = mx c+ is sometimes referred to as slope-intercept equation.
Equation of straight line can also be expressed in a general form. Referring equations
(1) and (2) which have same gradient, that is:
y y− 1 = y − 2 y 1 (4)
xx− 1 x − 2 x 1

Equation (4) can be rearranged to get,

(y − 2 y 1 )x − (x − 2 x 1 )y y x+ 1 2 − x y = 1 2 0

Since ,x 1 1 , y x 2 , and y are given real numbers, then
2
(y − 2 y 1 ), − (x − 2 x 1 ), and y x − 1 2 x y are also real numbers. Thus, they can be
1 2
replaced by constants a, b, and c, respectively. Therefore, the equation can be
reduced to
c
ax by+ += 0 (5)
Equation (5) is called the general equation of a straight line. Mathematics Form One

137

25/10/2024 09:51:52
Mathematics form 1.indd 137 25/10/2024 09:51:52
Mathematics form 1.indd 137