The equation of a straight line | Maths | Quizalize & Oak National Academy

Starter quiz

Which equations are represented by the bar model shown?
- $a + 7 = 20$ ✓
- $a + 20 = 7$
- $7 = 20 + a$
- $a = 20 - 7$ ✓
- $20 - a = 7$ ✓
Fill in the missing value for the $y$ intercept of this line $(0,$ ______ $)$ .
- '-4' ✓
Match up the coordinate with the relationship it satisfies.
- $(5,1)$
  
  ⇔
  
  $x + y = 6$ ✓
- $(-2,4)$
  
  ⇔
  
  $y = x + 6$ ✓
- $(8,2)$
  
  ⇔
  
  $x - y = 6$ ✓
- $(1,6)$
  
  ⇔
  
  $2x + y = 8$ ✓
- $(2,3)$
  
  ⇔
  
  $x + 2y = 8$ ✓
- $(1,3)$
  
  ⇔
  
  $2x + 2y = 8$ ✓
What is the gradient of this line?
- '7' ✓
Match up the expressions containing brackets with their expanded forms.
- $6(x + 4)$
  
  ⇔
  
  $6x + 24$ ✓
- $6(2x + 4)$
  
  ⇔
  
  $12x + 24$ ✓
- $4(2x + 1)$
  
  ⇔
  
  $8x + 4$ ✓
- $4(x + 1)$
  
  ⇔
  
  $4x + 4$ ✓
- $2(3x + 2)$
  
  ⇔
  
  $6x + 4$ ✓
- $6(2x - 4)$
  
  ⇔
  
  $12x - 24$ ✓
Fill in this coordinate, $(5,$ ______ $)$ , so it satisfies the equation $2x + 2y = 10$ .
- '0' ✓

Exit quiz

Match the keywords to their definitions.
- constant
  
  ⇔
  
  a term that does not vary ✓
- coefficient
  
  ⇔
  
  a numerical multiplier of a specific variable in a term ✓
- gradient
  
  ⇔
  
  a measure of how steep a line is ✓
- $y$ -intercept
  
  ⇔
  
  the coordinate where a line crosses the $y$ axis ✓
- origin
  
  ⇔
  
  the coordinate $(0,0)$ ✓
- equation of a straight line
  
  ⇔
  
  a relationship which, when plotted, forms a straight line ✓
Which of these relationships are represented by this bar model?
- $y - x = 5$
- $y + x = 5$
- $x - y = 5$ ✓
- $x = y + 5$ ✓
- $y = x - 5$ ✓
The graph shows 5 lines labelled A, B, C, D and E. Match the line to its gradient and $y$ intercept.
- A (purple)
  
  ⇔
  
  gradient $1\over 2$ , $y$ -intercept $(0,-2)$ ✓
- B (green)
  
  ⇔
  
  gradient $1\over 2$ , $y$ -intercept $(0,2)$ ✓
- C (pink)
  
  ⇔
  
  gradient $-2$ , $y$ -intercept $(0,-2)$ ✓
- D (blue)
  
  ⇔
  
  gradient $-{1\over 2}$ , $y$ -intercept $(0,2)$ ✓
- E (black)
  
  ⇔
  
  gradient $2$ , $y$ -intercept $(0,-2)$ ✓
Match the equations of lines to their key features.
- $y = 5x - 4$
  
  ⇔
  
  gradient $5$ , $y$ -intercept $(0,-4)$ ✓
- $y = 4 - 5x$
  
  ⇔
  
  gradient $-5$ , $y$ -intercept $(0,4)$ ✓
- $y = -4x - 5$
  
  ⇔
  
  gradient $-4$ , $y$ -intercept $(0,-5)$ ✓
- $y = 4x + 5$
  
  ⇔
  
  gradient $4$ , $y$ -intercept $(0,5)$ ✓
- $y = 5x + 4$
  
  ⇔
  
  gradient $5$ , $y$ -intercept $(0,4)$ ✓
- $y = 5 - 4x$
  
  ⇔
  
  gradient $-4$ , $y$ -intercept $(0,5)$ ✓
What are the key features of the graph with equation $y= 3(5 - 2x)$ ?
- gradient $15$ , $y$ -intercept $(0,-6)$
- gradient $6$ , $y$ -intercept $(0,-15)$
- gradient $-2$ , $y$ -intercept $(0,15)$
- gradient $-2$ , $y$ -intercept $(0,5)$
- gradient $-6$ , $y$ -intercept $(0,15)$ ✓
Which coordinates are on the line $2x - y = 5$ ?
- $(-2,-9)$ ✓
- $(-1,3)$
- $(0,5)$
- $(7,9)$ ✓
- $(10,5)$

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Lesson Details

Key learning points

Linear relationships can be written in a variety of algebraic forms.
It is possible to identify the gradient and y-intercept when the equation is written in the form y=mx+c.
The m comes from the French "monter" (to climb/ascend) and the c from "commencer" (to start).
Linear equations can be rearranged in order to reveal the gradient and y-intercept.

Common misconception

Pupils may think graphs are only linear if written in the form y=mx+c

Use the first learning cycle as an opportunity to show graphs in many formats. y=mx+c makes the gradient and y intercept clear.

Keywords

Equation of a line - Any equation whose graph forms a straight line.
Coefficient - A constant numerical multiplier of the variables in a term.
Constant - A term that does not change; it contains no variables.