Equation of a straight line

There are lots of different ways to represent a straight line - here’s a summary of a few of them.

y = mx + c

This is probably the way you’re familiar with. In this equation:

• m is the gradient (or slope) of the line. It’s the amount y changes for a unit (1) change in x.
• c is the y-intercept - the value of y when x = 0 and where the line crosses the y-axis.

This equation is useful if you know the gradient and y-intercept of a line, and want to find the value of y for a given x.

Ax + By + C = 0

This is called the general form of a straight line. In this equation:

• A, B, and C are constants (fixed numbers).

y - y_1 = m(x - x_1)

This is called the point-slope form of a straight line. In this equation:

• m is the gradient (or slope) of the line.
• (x, y) is any point on the line.
• (x_1, y_1) is another specific point on the line.

This essentially, more explicitly, describes how we get from one point on the line to another, using the gradient.

It’s useful when we know the gradient of the line and points on it, but don’t know the y-intercept.