# 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

$\begin{array}{l}y=-\frac{2}{3}x+\frac{1}{2}←\overline{)y=mx+c}\\ \therefore \text{Gradient}m=-\frac{2}{3}\\ \text{}y-\text{intercept},\text{}c=\frac{1}{2}\end{array}$