Problem solving with linear graphs | Maths | Quizalize & Oak National Academy

Starter quiz

What number is halfway between 7 and 19?

'13' ✓
Which of these coordinates are on the line $x = 2$ ?

(2, -2) ✓

(0, 2)

(-2, 2)

(2, 2) ✓

(2, 7.1) ✓
Which of these lines passes through the coordinates (2, 8) and (5, 8)?

$x = 2$

$x = 8$

$y = 5$

$y = 8$ ✓

$x + y = 10$
______ lines are straight lines which are always the same non-zero distance apart.

'Parallel' ✓
The gradient of this line is ______.

'3' ✓
The gradient of the line passing through (5, 5) and (9, -3) is ______.

'-2' ✓

Exit quiz

What is the coordinate of the midpoint of the line segment AB?

(4, 6)

(5, 4) ✓

(5, 5)

(6, 4)

(10, 8)
What is the coordinate of the midpoint of the line segment AB?

(-3, 2)

(1, 5) ✓

(2, 4)

(2, 6)

(3, 5)
Point P has coordinates (3, -8) and point Q has coordinates (10, -2). What is the coordinate of the midpoint of PQ?

(5, -5)

(5, -4)

(6, -6.5)

(6.5, -5) ✓

(7, -5)
Point A has coordinates (6, 2) and B has coordinates (12, 0). Line L has equation $y = 2x - 5.$ What is the equation of the line parallel to L which passes through the midpoint of AB?

$y = -5x-15$

$y = 9-5x$

$y = 8-2x$

$y = 2x-14$

$y = 2x-17$ ✓
If shape ABCD is a parallelogram, which of these statements would have to be true?

The line segments AB and BC have the same gradient.

The line segments AB and DC have the same gradient. ✓

The line segments AD and BC have the same gradient. ✓

The line segment AB has a smaller gradient than the line segment BC.
Jacob plots four points A, B, C on a graph. Jacob says he can join the points to form a parallelogram. Why is Jacob incorrect?

AB is not parallel to BC.

AD is not parallel to BC.

AB is not parallel to DC. ✓

The side lengths are not all the same length.

The midpoint of AC is different to the midpoint of BD.

Worksheet

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Video

Lesson Details

Key learning points

The shape of a graph can be used to identify its equation.
Either the graphs or the equations can be used to identify parallel lines.

Common misconception

Pupils may not appreciate all the steps required to prove what type of shape is shown.

A warm-up for the lesson could be to review properties of shapes. Consider describing a shape, one property at a time. How much information is needed before pupils can be certain they know which shape is being described?

Keywords

Midpoint - The midpoint of a line segment is halfway between the two end points.