Graphically solving two linear graphs that intersect | Maths

Starter quiz

The graph of a __________ equation is a straight line.
- arithmetic
- linear ✓
- quadratic
- variable
Which of these lines has the least steep gradient?
- Line a
- Line b
- Line c ✓
Use the graph of $y =3x-4$ to solve the equation $3x-4=2$ . The solution is $x=$ ______.
- '2' ✓
$Use the graph of <Math>y =7.4 x+12.95</Math> to estimate the value of <Math>7.4\times 4+12.95</Math>.$

Use the graph of $y =7.4 x+12.95$ to estimate the value of $7.4\times 4+12.95$ .
- 28
- 33
- 38
- 43 ✓
- 48
Aisha is plotting the graph of the line $3y + 4x=24$ . She only wants to plot two points. Which of these points would be the best points for Aisha to use?
- When $x=0$ ✓
- When $x=2$
- When $x=4$
- When $x=6$ ✓
- When $x=8$
Select the points which lie both on the line $y=2x+1$ and on the line $y=3x-2$ .
- (1, 3)
- (4, 10)
- (0, -2)
- (3, 7) ✓
- (2, 5)

The point where the lines $y=2x+4$ and $y=2-x$ meet is called the ______.
- answer
- intersection ✓
- solution
- variable
Izzy plots the graphs of $y=2x+1$ and $y=3x-2$ on the same coordinate grid. How many points will lie on both lines?
- '1' ✓
The linear equations $y = 2x + 5$ and $y = 2 − x$ intersect at the point with coordinates (−1, 3). What is the solution to the equation $2x+5=2-x$ ?
- $x=-1$ ✓
- $x=3$
- $y=-1$
- $y=3$
Use the graph to solve the simultaneous equations $y=2x-1$ and $y=3x-2$ .
- $x=2$ , $y=3$
- $x=7$ , $y=-2$
- $x=1$ , $y=1$
- $x=-2$ , $y=7$ ✓
- $x=3$ , $y=2$
The diagram shows 6 points and the the lines $y=2x-1$ and $y=5-x$ . Which points satisfy the inequality $y>2x-1$ ?
- A and C
- C and D
- A and D
- A, B and C ✓
- D, E and F
The diagram shows 6 points and the the lines $y=2x-1$ and $y=5-x$ . The point that is the region $y>5-x$ and $y<2x-1$ is ______.
- 'D' ✓

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There is only one way to solve linear equations; by manipulation and isolating the variable(s).

When we plot more than one linear equation on a graph we can use the intersection to find the solution.

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