5.4 Equation of a Straight Line

5.4 Equation of a Straight Line: y = mx + c

1. Given the value of the gradient, m, and the y-intercept, c, an equation 
of a straight line y = mx + can be formed.


2. If the equation of a straight line is written in the form y = mx + c, the 
gradient, m, and the y-intercept, c, can be determined directly from the 
equation.


Example:
Given that the equation of a straight line is y = 3 – 4x. Find the gradient and y-intercept of the line?
 
Solution:
y= 3 – 4x
y= – 4x + 3 ← (y = mx + c)
Therefore, gradient, m = – 4
y-intercept, c = 3


3. If the equation of a straight line is written in the form ax + by + c = 0, 
change it to the form y = mx + c before finding the gradient and the
y-intercept.

Example:
Given that the equation of a straight line is 4x + 6y– 3 = 0. What is the gradient and y-intercept of the line?

Solution:
4x + 6y – 3 = 0
6y = –4x + 3

y = 2 3 x + 1 2 y = m x + c Gradient m = 2 3 y intercept , c = 1 2
 

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