Finding the equation of the line ay + bx + c = 0 | Maths

Starter quiz

The equation of this line is: $y =$ ______ $- 2x$ .
- '3' ✓
This coordinate, (______, 0), lies on the line $y + x = 4$ . What is the missing $x$ coordinate?
- '4' ✓
This coordinate, (______, 0), lies on the line $y + x = 7$ . What is the missing $x$ coordinate?
- '7' ✓
Which of these coordinates lie on the $x$ axis?
- (0,0) ✓
- (0,4)
- (4,0) ✓
- (0, 0.3)
- (0.9,0) ✓
Which of these equations could be represented by this bar model?
- $y = 5x - 8$ ✓
- $5x = y + 8$ ✓
- $y - 8 = 5x$
- $8 + 5x = y$
- $8 = 5x - y$ ✓
Which of these equations are written in the form $y = mx + c$ ?
- $y + x = 10$
- $y = 5x + 1$ ✓
- $x = 5$
- $y = 7 - 3x$ ✓
- $y = x$ ✓

The graph shows 5 lines labelled A, B, C, D and E. Match the lines to the equations.
- A (green)
  
  ⇔
  
  $x = -4$ ✓
- B (blue)
  
  ⇔
  
  $y = {1\over 3}x - 4$ ✓
- C (black)
  
  ⇔
  
  $y = -4$ ✓
- D (pink)
  
  ⇔
  
  $y = {1\over 3}x + 4$ ✓
- E (purple)
  
  ⇔
  
  $y = -{1\over 3}x + 4$ ✓
Which equations are represented in this bar model?
- $y= 2x - 4$
- $2x + y + 4 = 0$
- $y = 2x + 4$ ✓
- $y = 4 - 2x$
- $2x + 4 - y = 0$ ✓
Which equations are represented in this bar model?
- $y = 4x - 2$ ✓
- $4x- y + 2 = 0$
- $y = 4x + 2$
- $y - 4x + 2 = 0$ ✓
- $4x - y - 2 = 0$ ✓
Match the $y$ -intercepts to the correct graph in the form $y + x + c = 0$
- (0, -7)
  
  ⇔
  
  $y + x + 7 = 0$ ✓
- (0, 7)
  
  ⇔
  
  $y + x - 7 = 0$ ✓
- (0, -10)
  
  ⇔
  
  $y - x + 10 = 0$ ✓
- (0, 10)
  
  ⇔
  
  $y - x - 10 = 0$ ✓
- (0,1)
  
  ⇔
  
  $y + x - 1 = 0$ ✓
- (0,-1)
  
  ⇔
  
  $y - x + 1 = 0$ ✓
Match the $x$ -intercepts to the correct graph in the form $y + x + c = 0$
- (-3,0)
  
  ⇔
  
  $y + x + 3 = 0$ ✓
- (3,0)
  
  ⇔
  
  $y + x - 3 = 0$ ✓
- (5, 0)
  
  ⇔
  
  $y - x + 5 = 0$ ✓
- (-5,0)
  
  ⇔
  
  $y + x + 5 = 0$ ✓
- (4,0)
  
  ⇔
  
  $x + y - 4 = 0$ ✓
- (-4,0)
  
  ⇔
  
  $x - y + 4 = 0$ ✓
Which of these are the correct $x$ and $y$ -intercepts for the equation $3x + y - 6 = 0$ ?
- (6,0) and (0,6)
- (-6,0) and (0,-6)
- (2,0) and (0,2)
- (2,0) and (0,6) ✓
- (6,0) and (0,-2)

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To draw the graph using the gradient and intercept you can just count the squares.

Encourage pupils to look at the scales on the axes carefully when drawing a line given the gradient and y-intercept.

Equation of a line - An equation of a line is any equation whose graph forms a straight line.