Gradient of a line

The Maths Habit

Which hill is harder to walk up?

ABB. It is steeper: it goes up more for each step across.

How many squares from A to B?AB4 squares
How many squares from C to D?CD3 squares

Gradient
How steep a line is.
Steep
Going up a lot for a small step across.
Horizontal
Going straight across, flat.
Vertical
Going straight up.

Work out the gradient of the line.

123456123456780xy12
upacross=21=2
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy14
upacross=41=4
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy12
upacross=21=2
1Draw the step.
2Count across and up.
3Divide up by across.
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy13
upacross=31=3

Work out the gradient of the line.

123456123456780xy12
upacross=21=2
1Draw the step.
2Count across and up.
3Divide up by across.
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy15
upacross=51=5

Work out the gradient of the line.

123456123456780xy12
upacross=21=2
1Draw the step.
2Count across and up.
3Divide up by across.
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy12
upacross=21=2

Work out each one.

6 ÷ 23
8 ÷ 42
9 ÷ 33

Work out the gradient of the line.

123456123456780xy24
upacross=42=2
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy33
upacross=33=1
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy24
upacross=42=2
1Draw the step.
2Count across and up.
3Divide up by across.
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy26
upacross=62=3

Work out the gradient of the line.

123456123456780xy24
upacross=42=2
1Draw the step.
2Count across and up.
3Divide up by across.
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy36
upacross=63=2

Work out the gradient of the line.

123456123456780xy24
upacross=42=2
1Draw the step.
2Count across and up.
3Divide up by across.
1Draw the step.
2Count across and up.
3Divide up by across.

Work out the gradient of the line.

123456123456780xy22
upacross=22=1

Thumbs up for yes. Thumbs down for no.

  1. Up 6, across 2. The gradient is 3.

    Yes
  2. Up 4, across 2. The gradient is 8.

    No: 4 ÷ 2 = 2
  3. Up 3, across 3. The gradient is 1.

    Yes
  4. Up 9, across 3. The gradient is 6.

    No: 9 ÷ 3 = 3
  5. Up 8, across 2. The gradient is 4.

    Yes

Gradient of a line worksheet, page 1

Gradient of a line worksheet, page 2

Answer sheet

  1. A line goes down 2 for each 1 across. What is its gradient?

    −2
  2. A line goes up 1 for every 2 across. What is its gradient?

    ½
  3. A line goes through (1, 2) and (4, 14). Work out its gradient without drawing it.

    12 ÷ 3 = 4
  4. Line A has a gradient of 3. Line B goes up 10 for 2 across. Which line is steeper?

    B: 10 ÷ 2 = 5

  1. Work out the gradient of the line.

    3
    12342460xyupacross=2=
  2. Work out the gradient of the line.

    4
    12342460xyupacross==
  3. Work out the gradient of the line.

    Gradient 2
    12342460xy
Exit tickets to print