1. Millburn Academy
Maths department
Higher
Equation of a Line
y = mx + c

2. where m is the gradient and c is the y-intercept.
In National 5 you learned that the equation of a straight line is given by the formula:
y = mx + c
where m is the gradient and c is the y-intercept. O
eg the line y = 2x - 1
crosses the y axis at (0,-1)
and has a gradient of 2.

3. What is the gradient of a horizontal line?
Horizontal Lines
What is the gradient of a horizontal line?
Since this horizontal line has a gradient of 0 and it crosses the y axis at the point (0,2) its equation is: O
y = 0x + 2
simplified
y = 2
All horizontal lines have an equation of the form y = k
where k is the y-intercept.
ie all point on a horizontal line have the same y coordinate.

4. ∞ Vertical Lines What is the gradient of a vertical line?
All points on a vertical line have the same x-coordinate.
In this example all points have an x-coordinate of 3. O
Therefore the equation of this line is x = 3
All vertical lines have an equation of the form x = k
where k is the point of intersection with the x-axis..

5. Horizontal lines have equation: y = k
Summary
Horizontal lines have equation: y = k
where k is the point
of intersection with
the y-axis. O
Vertical lines have
equation: x = k
Sloping lines have equation:
y = mx + c
where k is the point of intersection with the
x-axis.
where m is the gradient and c is the y intercept

6. General Form of the Linear Equation
The equation of the line is:
We can rearrange this into the form: ax + by + c = 0
This is the general form of a linear equation. O