Page 126 - Mathematics

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.

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 or slope. That is, it can be horizontal, vertical or slanted. The concept
of gradient or slope is applicable in many real-life activities such as lifting heavy
Tanzania Institute of Education
loads, 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 or slope is a measure of steepness of a straight line and it is usually
denoted by m. 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
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Mathematics form 1.indd 120
Mathematics form 1.indd 120 25/10/2024 09:51:45