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

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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.