Page 131 - Mathematics

Example 6.6

4
The gradient of the line passing through the points P(3, 5) and Q(x, 1) is .
Find the value of x. 3
Solution Tanzania Institute of Education

Given the points P (3, 5) and Q (x, 1). The gradient of the line joining the
two points is given by,

y − y
m = 2 1
x − x 1
2
4
5
But, x = , x x = 3, y = 1, y = and m = . Substitute these values into the
1
2
2
1
formula for slope to get, 3
4 = 51−
3 3 x−
4 = 4
3 3 x−
Cross multiplication gives,

4(3 x− ) 12=

12 4x− = 12
4x− = 0

Therefore, the value of x is 0.

In Examples 6.3, 6.4, and 6.5, it can be observed that the values of the gradient

are non-zero. Thus, only slanted lines have non-zero gradients. Moreover, a line
slants towards right ! ( ) if its gradient is positive as in Example 6.4 and slants

towards left ! ( ) if the gradient is negative as in Example 6.5.

However, horizontal and vertical lines have unique gradients. If the line is horizontal,
the change in y-values is zero and the gradient of the line is zero, as shown by the Mathematics Form One
line DE in Figure 6.3.

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Mathematics form 1.indd 125