Two points make a line

The idea

A linear equation y = ax + b is plotted as a straight line by finding any two points on it, plotting them on the coordinate plane, joining them and extending the line both ways.

Drawing y = 2x + 1

The equation y = 2x + 1 gives a y for every x. All those points lie on one straight line. You want to draw it with a ruler.

How many points do you think you need on the line before you can draw all of it?

• Just one
• Two
• As many as possible

Plot and join

Choose an x. The equation gives the y. Plot the point, plot another, then Join them.

Two points are enough

To plot y = ax + b, find any two points on it, plot them on the coordinate plane, join them and extend the line in both directions.

For y = 2x + 1: when x = 0, y = 1, so A (0, 1) is on the line. When x = 3, y = 7, so B (3, 7) is on it. Plot A and B, join them with a ruler, and carry the line on both ways.

Notes

To plot a linear equation: find two points, plot them, join them and extend the line both ways.

Check yourself

What is the least number of points you need to draw the line y = ax + b?

To plot y = 3x − 1, you take x = 2. What is y?

Answer: 5

3 × 2 − 1 = 6 − 1 = 5, so (2, 5) is a point on the line.

Which two points are both on the line y = x + 4?

You have plotted two points of y = ax + b. What do you do next?

• Two — correct. Yes. Two points fix a straight line.
• One. Many lines pass through one point. A second point fixes the line.
• Five. Five is more than you need. Two points are enough.
• (0, 4) and (1, 4). When x = 1, y = 1 + 4 = 5, not 4.
• (0, 4) and (1, 5) — correct. Yes. 0 + 4 = 4 and 1 + 4 = 5.
• (1, 5) and (2, 5). When x = 2, y = 2 + 4 = 6, not 5.
• Stop: the two points are the whole line. The line goes on and on. Extend it both ways.
• Join them, but only between the two points. Extend the line past both points: it never ends.
• Join them and extend the line in both directions — correct. Yes. The line goes on past both points.