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## Background

We assume that you are familiar with the Cartesian coordinate system and solving linear equations.

Functions which have straight line graphs are called linear functions (for the obvious reason). These functions can always be written in the form (To see why click here.) The set of points given by the ordered pairs that satisfies the above equation is a straight line.

## Finding Points on a Line

To find points on the line y = mx + b,

• choose x and solve the equation for y, or
• choose y and solve for x.

### Example 1.

Find two points on the line y = 2x + 1:

Point 1 - Choose x and solve for y:

Let x =1. Substitute x = 1 into y = 2x + 1 and solve for y.

y = 2(1) + 1 = 2 + 1 = 3

Hence (1,3) is one point on the line y = 2x + 1.

Point 2 - Choose y and solve for x:

Let y = -3. Substitute y = -3 into y = 2x + 1 and solve for x.

 -3 = 2x + 1 (Subtract 1 from both sides) -4 = 2x (Divide both sides by 2) -2 = x

Hence (-2,-3) is another point on the line y =2x+1.

### Exercise 1.

Follow the above example and try some of the following exercises:

Locate points on the line defined by y = x +

 x y

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