Key ideas
Table of values
Pick some x values (like −1, 0, 1, 2).
Put each one into the equation to find y.
Each pair (x, y) is a point on the line.
Sketching the line
Plot the points, then join them with a ruler and extend the line to the edges of the grid.
If the points don't line up, check your table.
Horizontal lines
Every point has the same y-coordinate.
The equation is y = a number, like y = 3.
Vertical lines
Every point has the same x-coordinate.
The equation is x = a number, like x = −2.
Tables of values
Complete the table of values for y = 2x + 1.
(2 marks)
| x | −1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
Put each x value into the equation.x = −1: y = 2 × (−1) + 1 = −1x = 0: y = 2 × 0 + 1 = 1✓1x = 1: y = 2 × 1 + 1 = 3x = 2: y = 2 × 2 + 1 = 5
In plain EnglishReplace x with each number in turn. Use a bracket for the negative.
Fill in the table.
Check: y goes up by 2 each time ✓✓2
| x | −1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y | −1 | 1 | 3 | 5 |
In plain EnglishThe y values go up by the same amount each time. That means the points will lie on a straight line.
Sketching a line from its equation
Draw the line y = 2x + 1.(2 marks)
Plot the points from the table.(−1, −1), (0, 1), (1, 3), (2, 5)✓1
In plain EnglishEach column of the table gives a point: across x, then up or down y.
Join them with a ruler.Label the line✓2
In plain EnglishDraw a straight line through all the points and extend it to the edge of the grid. Label it with its equation.
Horizontal lines
Write down the equation of this line.(1 mark)
What do the points have in common?(−3, 2), (0, 2), (4, 2): every y-coordinate is 2y = 2✓1
In plain EnglishPick some points on the line. The x-coordinates change, but y is always 2.
⚠ A common mistake: writing x = 2 for a horizontal line. Horizontal lines are y = …
Vertical lines
Draw the line x = 3.(1 mark)
Every point has x = 3.Points like (3, −2), (3, 0), (3, 3)✓1
In plain EnglishPlot some points with x-coordinate 3, then join them. The line goes straight up and down through 3 on the x-axis.
0 of 0 complete
Your turn
For drawing questions, complete the table of values first: your coordinates appear underneath it. Then tap the grid to plot them (tap again to remove one), or type them in the box. The line is drawn through your points. Stuck? Tap Need a hint?