Is the point on the line?

The idea

If a point lies on a line, its coordinates satisfy the equation of the line, so substituting the coordinates checks whether a point lies on the line.

A point off the grid

The line y = 2x + 1 is drawn. The point (7, 15) is far off the edge of the grid, so you cannot see whether it is on the line.

How could you tell whether (7, 15) is on the line without drawing more of the grid?

• Measure it with a ruler
• Put the numbers into the equation
• Guess

Test the points

Tap each point. The toy puts its x into 2x + 1 and compares with its y.

Substitute and compare

If a point lies on a line, its coordinates satisfy the equation of the line. To check a point, substitute its x and y into the equation.

To check (7, 15) on y = 2x + 1: put x = 7. Then 2 × 7 + 1 = 15, and the point has y = 15. They match, so (7, 15) is on the line. For (7, 16) they would not match, so it would not be on the line.

Notes

A point is on a line if its coordinates satisfy the equation. Substitute x and y to check.

Check yourself

Is (7, 15) on y = 2x + 1? Put x = 7. What does 2x + 1 give?

Answer: 15

2 × 7 + 1 = 15, which is the y of the point. So (7, 15) is on the line.

Which point lies on the line y = 3x − 2?

Does (2, 9) lie on the line y = 4x + 1?

The point (3, k) lies on the line y = 2x + 1. What is k?

Answer: 7

y = 2 × 3 + 1 = 7, so k = 7.

• (2, 4) — correct. Yes. 3 × 2 − 2 = 4, which matches.
• (2, 5). 3 × 2 − 2 = 4, not 5.
• (1, 2). 3 × 1 − 2 = 1, not 2.
• No, because 4 × 2 + 1 = 8. 4 × 2 + 1 is 9, not 8.
• Yes, because 4 × 2 + 1 = 9 — correct. Yes. The equation gives y = 9 when x = 2, the same as the point.
• No, because 2 + 9 = 11. Adding the coordinates does not test the equation. Put x into 4x + 1 instead.