The equation of a straight line
I can appreciate that writing linear equations in the form y = mx + c helps to reveal the structure.
The equation of a straight line
I can appreciate that writing linear equations in the form y = mx + c helps to reveal the structure.
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.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Video
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Starter quiz
6 Questions
$$(5,1)$$ -
$$x + y = 6 $$
$$(-2,4)$$ -
$$ y = x + 6 $$
$$(8,2)$$ -
$$x - y = 6$$
$$(1,6)$$ -
$$2x + y = 8$$
$$(2,3)$$ -
$$x + 2y = 8 $$
$$(1,3)$$ -
$$ 2x + 2y = 8 $$
$$6(x + 4)$$ -
$$6x + 24$$
$$6(2x + 4)$$ -
$$12x + 24$$
$$4(2x + 1)$$ -
$$8x + 4$$
$$4(x + 1)$$ -
$$4x + 4$$
$$2(3x + 2)$$ -
$$6x + 4$$
$$6(2x - 4)$$ -
$$12x - 24$$
Exit quiz
6 Questions
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
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 $$(0,-2)$$
$$y = 5x - 4$$ -
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 $$(0,5)$$