| To establish a rule for the equation of a
straight line, consider the previous example.
An increase in distance by 1 km results in an
increase in cost of $3. We say that the rate of change of cost with
respect to distance is $3 per kilometre.
The information given in the graph can be represented by the equation c
= 5 + 3d. That is:
In general:
A line with equation y = mx + c has gradient m
and y-intercept c.
The gradient of a straight line is the coefficient of x.
Particular Case
If a straight line passes through the origin, then its y-intercept
is 0. So, the equation of a straight line passing through the origin
is
y = mx
where m is the gradient of the line.
Example 7
Solution:
Example 8
Write down the equation of the straight line that has m = 5 and c
= 3.
Solution:
Example 9
Calculate the gradient of the straight line given in the following
diagram; and find its equation.
Solution:
Example 10
Find the equation of the line joining the points (2, 3) and (4,7).
Solution:
Key Terms
equation of a straight line, gradient,
y-intercept |
