Page 127 - Mathematics

the triangle. The length of the vertical side BC of the triangle is the difference in
y-coordinates of the points B and C, that is, y − y or y − . y The length of the
2 1 1 2
horizontal side of the triangle is the difference in x-coordinates of the points A and
x
C, that is x − or x − x 2 . Tanzania Institute of Education
1
2
1

Figure 6.2: A straight line AB with horizontal and vertical changes

From Figure 6.2, the gradient m of the straight line AB is determined by using the
following formula:

change in (vertical increase)
=
change in (horizontal increase)
y − y y − y
Thus, m = 2 1 = 1 2 .
x − 2 x 1 x − 1 x 2
The following are the procedures for calculating the gradient of a straight line
joining two points A(x , y ) and B( ,xy ).
1 1 2 2 y − y
2
1. Write down the formula for calculating the gradient, m = x − x 1 .
2. Assign values to (x , y ) and (x , y ) . 2 1
1 1 2 2
3. Substitute the values into the formula to obtain the gradient .m

4. Write the final answer which is the gradient .m

Note:
When finding the gradient, the order of finding the difference between the Mathematics Form One
coordinate values in the formula does not matter. One may choose to find the
difference from the second point or may choose to find the difference from
the first point provided that the coordinates are subtracted correspondingly.

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