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.