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 + 3*d*. 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:
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Example 8
Write down the equation of the straight line that has *m* = 5 and *c* = 3.
##### Solution:
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Example 9
Calculate the gradient of the straight line given in the following
diagram; and find its equation.
##### Solution:
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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 |