Page 127 - Mathematics_F1

10. The trapezium is formed using the points A( − 2, − 2), B(5, 2),− B(5, 2),−
and D(4,3). Use the given points to draw the trapezium and determine
its height by counting the number of unit boxes.

FOR ONLINE READING ONLY
Gradient of a straight line
A straight line is formed by joining two distinct points. Any two points lying on
the straight line can be used to define it. The nature of the straight line is described
by its gradient. That is, it can be horizontal, vertical or slanted. The concept of
gradient is applicable in many real-life activities such as lifting heavy loads,
Tanzania Institute of Education
climbing mountains, determining steepness during road construction and many
other applications. Engage in Activity 6.2 to learn how to recognise the gradient
of a straight line.

Activity 6.2: Recognising the gradient of a straight line

1. Use a graph paper to plot the points A (2, 1), B (5, 6), C (2, 7), and
D(6, 1) on the same xy-plane.
2. Find the difference between the x-coordinates and between

y-coordinates of AB, CD, BA, and DC.
3. Find the ratio of the difference of y-coordinates to x-coordinates obtained
in task 2.
4. The relationship between the ratios obtained in step 3 is called the gradient
of a line.
5. Explain how the value obtained in task 3 determines the nature of a line.

A gradient is a measure of steepness of a straight line and it is usually denoted
by m. The other name of gradient is slope. In coordinate geometry, the standard
way to define the gradient of a straight line is by finding the ratio between the
change in y (vertical increase) to the change in x (horizontal increase), that is,
Mathematics Form One Consider a line passing through the points A(x , y ) and B(x , y ) Also, consider
change in y
coordinates
Gradient, m =
coordinates
change in x

1
2
2
1
a right-angled triangle ABC with the straight line AB shown in Figure 6.2. The
gradient of a line passing through points A and B is determined by the ratio of
the length of the vertical side of the triangle to the length of the horizontal side of
120

25/09/2025 15:01:30
Mathematics form 1.indd 120
Mathematics form 1.indd 120 25/09/2025 15:01:30