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Year 8

Solving linear equations graphically using technology

I can explore how to solve linear equations graphically via dynamic software.

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Share activities with pupils
New
New
Year 8

Solving linear equations graphically using technology

I can explore how to solve linear equations graphically via dynamic software.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A linear expression expressed on a graph represents a straight line.
  2. This line can be used to find one variable when given the other.
  3. A horizontal or vertical line represents a particular value of a variable.
  4. Where this meets the linear graph the solution of a linear equation.

Common misconception

That we always have to use written methods to solve equations.

Use Desmos to show that equations like $$3x-1=17$$ and $$3x-1=x+9$$ can be solved by drawing both lines and finding the intersection.

Keywords

  • Equation - An equation is used to show two expressions that are equal to each other.

  • Solution - The solution to an equality is the value which, when substituted, maintains the equality between expressions.

Ask pupils as a starter to solve $$3x-1=17$$ and $$3x-1=x+9$$ using pen and paper then later ask them to solve using graphing in Desmos. Ask them to explain why their solutions work both graphically, and algebraically.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
$$x=5$$ is the to the equation $$7x-3=32$$
Correct Answer: solution, Solution
Q2.
Which is the solution to the equation $$16-3x=7$$?
$$x=-3$$
Correct answer: $$x=3$$
$$x=7$$
$$x=9$$
Q3.
The relationship $$y=2x+6$$ when plotted produces a graph.
bar
curved
Correct answer: linear
parabolic
Q4.
Andeep plots the graph of the equation $$y=3x-10$$. What is the $$y$$ coordinate when the $$x$$ coordinate is $$-5$$?
Correct answer: $$-25$$
$$-15$$
$$-5$$
$$5$$
$$25$$
Q5.
Find the coordinates of the point where the lines $$y=5-x$$ and $$y=2x-1$$ intersect.
An image in a quiz
$$(5, 0)$$
$$(0, 5)$$
$$(-1, 0)$$
Correct answer: $$(2, 3)$$
Q6.
What is the $$x$$ coordinate of this point?
An image in a quiz
Correct answer: $$2\frac{1}{2}$$
$$1.25$$
Correct answer: $$2.5$$
$$2\over5$$
Correct answer: $$5\over2$$

Exit quiz

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6 Questions

Q1.
This graphical representation shows that $$x=2$$ is the to the equation $$3x-2=4$$
An image in a quiz
Correct Answer: solution, Solution
Q2.
Use this graphical representation to solve the equation $$7-3x=-5$$
An image in a quiz
$$x=-5$$
$$y=-5$$
Correct answer: $$x=4$$
$$y=4$$
Q3.
Use this graphical representation to solve the equation $$3x+1={1\over2}x-4$$
An image in a quiz
Correct answer: $$x=-2$$
$$x=-5$$
$$y=-2$$
$$y=-5$$
Q4.
This graph shows that $$x=-2$$ is the solution to the equation $$5x+13=1-x$$ and that $$3$$ is the value of the when they are equal.
An image in a quiz
unknowns
Correct answer: expressions
equations
variables
Q5.
Solve $$2.7x+1=2.7x-5.4$$
An image in a quiz
$$x=1$$
$$x=2$$
$$x=2.7$$
Correct answer: There is no solution.
Q6.
Use the graphical representation to solve the equation $$3x+4=x-4$$
An image in a quiz
Correct answer: $$x=-4$$
$$x=-8$$
$$x=2$$
$$x=10$$
$$x=6$$