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Checking and securing understanding of interpreting graphs

Lesson details

Learning outcome

I can read and interpret points from a graph to solve problems.

Key learning points

  1. If you have one value, you can use a linear graph to find its pair.
  2. The pair of values will satisfy the linear equation.
  3. If the x and y variables have context, then their values can be interpreted within that context.
  4. With quadratic graphs, there may be more than one value to find.

Keywords

  • Quadratic - A quadratic is an equation whereby the highest exponent of the variable is 2; the graph of which forms a parabola.

  • Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

Common misconception

Substituting with negative values.

Putting brackets around all substituted values is good practice.

Teacher tip

Pupils could check answers, or explore quadratic graphs further, using technology.

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
except where otherwise stated. See Oak's terms & conditions
(Collection 2).

Lesson video

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Prior knowledge starter quiz

6 Questions

Q1.
Which pair of coordinates does not sit on the line $$y = 2x + 1$$?

(0, 1)
(1, 3)
(2, 5)
Correct answer: (3, 6)

Q2.
Which point is not on the line represented by $$y = -x - 2$$?

Correct answer: (-1, 1)
(0, -2)
(1, -3)
(2, -4)

Q3.
Which of these coordinates does not lie on the line $$y = 0.5x + 2$$?

(2, 3)
(4, 4)
(6, 5)
Correct answer: (8, 5)

Q4.
Which pair of coordinates is not a solution to the equation $$x^2 - y^2 = 16$$?

(5, 3)
(4, 0)
Correct answer: (6, 2)

Q5.
Which coordinate pair does not satisfy the quadratic equation $$y = x^2 - 4x + 3$$?

(1, 0)
(3, 0)
(2, -1)
Correct answer: (0, 5)

Q6.
Which point does not satisfy the equation $$2x^2 + 3x - 5 = y$$?

(-10, 165)
(-8, 99)
(1, 0)
Correct answer: (-1, 0)

6 Questions

Q1.
Which of the following coordinate pairs satisfies the equation $$2x + 5y = 58$$?

$$(-1, 10)$$
Correct answer: $$(-1, 12)$$
$$(1, 11)$$
$$(1, -11)$$

Q2.
Which of the following coordinate pairs satisfies the equation $$6x + 2y = 26$$?

$$(-2, 7)$$
$$(2, -7)$$
Correct answer: $$(2, 7)$$
$$(-2, -7)$$

Q3.
Which of the following coordinate pairs satisfies the equation $$5x = 1 - 2y$$?

$$(-1, -3)$$
Correct answer: $$(-1, 3)$$
$$(-1, -3)$$
$$(1, 3)$$

Q4.
Which of the following coordinate pairs satisfies the equation $$5x + 2y = 54$$?

Correct answer: $$(8, 7)$$
$$(-8, 7)$$
$$(8, -7)$$
$$(-8, -7)$$

Q5.
If $$x = 2$$, what is the value of $$y$$ for $$5x + 2y = -8$$?

Correct Answer: y = -9, -9

Q6.
If $$x = 2$$, what is the value of $$y$$ for $$5x + 2y = 32$$?

Correct Answer: 11, y = 11

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