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 + c 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=mx+c  Gradient m= 2 3      yintercept, c= 1 2