Solving linear equations graphically using technology | Maths

Starter quiz

$x=5$ is the ______ to the equation $7x-3=32$
- 'solution' ✓
Which is the solution to the equation $16-3x=7$ ?
- $x=-3$
- $x=3$ ✓
- $x=7$
- $x=9$
The relationship $y=2x+6$ when plotted produces a ______ graph.
- bar
- curved
- linear ✓
- parabolic
Andeep plots the graph of the equation $y=3x-10$ . What is the $y$ coordinate when the $x$ coordinate is $-5$ ?
- $-25$ ✓
- $-15$
- $-5$
- $5$
- $25$
Find the coordinates of the point where the lines $y=5-x$ and $y=2x-1$ intersect.
- $(5, 0)$
- $(0, 5)$
- $(-1, 0)$
- $(2, 3)$ ✓
What is the $x$ coordinate of this point?
- $2\frac{1}{2}$ ✓
- $1.25$
- $2.5$ ✓
- $2\over5$
- $5\over2$ ✓

This graphical representation shows that $x=2$ is the ______ to the equation $3x-2=4$
- 'solution' ✓
Use this graphical representation to solve the equation $7-3x=-5$
- $x=-5$
- $y=-5$
- $x=4$ ✓
- $y=4$
$Use this graphical representation to solve the equation <Math>3x+1={1\over2}x-4</Math>$

Use this graphical representation to solve the equation $3x+1={1\over2}x-4$
- $x=-2$ ✓
- $x=-5$
- $y=-2$
- $y=-5$
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.
- unknowns
- expressions ✓
- equations
- variables
Solve $2.7x+1=2.7x-5.4$
- $x=1$
- $x=2$
- $x=2.7$
- There is no solution. ✓
Use the graphical representation to solve the equation $3x+4=x-4$
- $x=-4$ ✓
- $x=-8$
- $x=2$
- $x=10$
- $x=6$

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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.

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.