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.
These resources will be removed by end of Summer Term 2025.
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.
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.
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.
Licence
Starter quiz
6 Questions
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1702397086%2Fdkk8dn5kaupijh2obcjo.png&w=828&q=75)
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1702397087%2Fvzb0bgaelxa5gz4mtysu.png&w=640&q=75)
$$(5,1)$$ -
$$x + y = 6 $$
$$(-2,4)$$ -
$$ y = x + 6 $$
$$(8,2)$$ -
$$x - y = 6$$
$$(1,6)$$ -
$$2x + y = 8$$
$$(2,3)$$ -
$$x + 2y = 8 $$
$$(1,3)$$ -
$$ 2x + 2y = 8 $$
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1702397091%2Fan5lv1ta2v6fsc05le6q.png&w=384&q=75)
$$6(x + 4)$$ -
$$6x + 24$$
$$6(2x + 4)$$ -
$$12x + 24$$
$$4(2x + 1)$$ -
$$8x + 4$$
$$4(x + 1)$$ -
$$4x + 4$$
$$2(3x + 2)$$ -
$$6x + 4$$
$$6(2x - 4)$$ -
$$12x - 24$$
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
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1702397085%2Fkikllzmgzvbbtazttqx6.png&w=640&q=75)
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1702397086%2Fixrihzxy1in8b7eo0ei7.png&w=640&q=75)
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 $$(0,5)$$