Page 138 - Mathematics

Equation (3) is an equation of a straight line passing through points P( ,xy and
)
1
1
Q( ,xy 2 with m as the gradient and c is the value of y at the point where the line
)
2
crosses y-axis. In this case, y-intercept is point (0, c) since the line will intersect
the y-axis if the x-coordinate is 0.
The x-intercept (a point where the line intersects the x-axis) is found when the
0
y-coordinate is 0. Setting = in y = mx c+ and solving for x gives,
y = mx c+
0 = mx c+
c
Tanzania Institute of Education
x = − m
 c 
Thus, the x-intercept is − m ,0 .


 
In general, if two points (,xy and (,xy lie on a straight line, then any other
)
)
1
2
1
2
point (x, y) on a line can be used to obtain the equation of the straight line using
the formula,
y y− 1 = y − 2 y 1
xx− 1 x − 2 x 1
Example 6.9

Find the equation of a straight line passing through the points (− 4, 3) and
(1, −7).

Solution
The equation of a straight line passing through points (x , y ) and (x , y )
1
2
2
1
is obtained by using the relation: y y− 1 = y − 2 y 1 , where (x, y) is any other
−
point on the line. xx 1 x − 2 x 1
and ( ,xy
) (1, 7).=
Let ( , ) ( 4, 3)xy = − 1 3, and y = − 7. − It follows that
2
2
1
1
Mathematics Form One Thus, x − − 3 = − = 10 −−
−
x =
4, x =
1, y =
2
2
1
y −
73
( 4)
1 ( 4)
− −
3
y −

x +
5
4
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25/10/2024 09:51:50
Mathematics form 1.indd 132 25/10/2024 09:51:50
Mathematics form 1.indd 132