Describe the Graph of Y Mx Where M 0

y=mx+c

Here we will learn about

y = mx + c

including how to recognise the gradient and
y-intercept from the equation


y = mx + c

and rearrange an equation into the standard grade of


y = mx + c
.

At that place are besides

y = mx + c

worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go side by side if you’re yet stuck.

What is y=mx+c?

The equation


y = mx + c


is the general equation of any direct line where

m

is the
slope
of the line (how steep the line is) and

c

is the
y-intercept
(the point in which the line crosses the
y-centrality).

y = mx + c
is a
linear
equation and the variables
10
and
y
relate to coordinates on the line.
When nosotros input a value for
10
into the equation

y = mx + c
, we get a upshot for
y.
This means that
ten
is an
independent variable, and
y
is a
dependent variable
every bit it is determined by the value of
ten.

E.g.

Let’s look at the line
y = 2x + i.

This graph has a

gradient

of

2

and a y-intercept of

1
, the coordinate (0,ane).

• The term
  linear
  is used to describe a straight line where the variables are raised to a power no higher than
  ane
• If the variables are raised to a power no higher than
  2
  we refer to it every bit a
  quadratic
• If the variables are raised to a power no higher than
  3
  nosotros refer to it equally a
  cubic, and so on.

The gradient ‘one thousand’

The gradient of the line tells usa
how steep the line is.

We utilize the alphabetic character

grand

to denote the gradient.

Imagine climbing a ladder. If the ladder is really close to the wall, the gradient of the ladder is really steep (you would near be climbing vertically). Taking the base of the ladder away from the wall means that the gradient of the gradient decreases reaching a lower point on the wall.

The bigger the gradient the steeper the line.

E.thousand.
A slope of
2
will generate a line that is much steeper than the gradient of

{\frac{1}{3}}
.

Meet the diagram below.

The slope of a line can exist many different types of number, i.e. fractions, decimals, negatives etc.

The y-intercept ‘c’

The

y-intercept
is the indicate of
intersection
between the straight line


y = mx + c
, and the
y-axis. The
y-intercept is the value of
y
when
x = 0.

Eastward.m.
Let’south look at the equation
y = 5x + vii.

To find the
y
intercept we substitute
x = 0
into the equation.

\brainstorm{aligned} &y=(five \times 0)+7\\\\ &y=7 \end{aligned}

So when
ten = 0, y = vii,
giving united states the coordinate
(0,vii).

This is the
y-intercept.

Here is a quick summary of some equations in the form


y = mx + c

with the gradient and
y
intercept highlighted.

How to use y=mx+c

In club to state the gradient and
y-intercept of a line:

1. Rearrange the equation to make
   y
   the subject
2. Substitute
   x = 0
   into the equation to find the
   y-intercept
3. Land the coefficient of
   ten
   (the gradient)

y = mx + c examples

Example 1: y=mx+c course

State the slope and
y-intercept of the line
y = −3x + 8.

1. Rearrange the equation to make
   y
   the subject field

The equation
y = −3x + 8
is already in the general form of


y=mx+c

so we can progress to pace
2
straight away.

ii
Substitute
x = 0
into the equation to find the
y-intercept

When
x = 0,

\begin{aligned} &y=(-three\times{0})+eight\\\\ &y=0+8\\\\ &y=viii \end{aligned}

The
y-intercept of the line
y = −3x + 8
is
eight, or
c = 8.

three
State the coefficient of
x
(the gradient)

The coefficient of
x
is
−iii.

The gradient of the line
y = −3x + eight
is
−iii, or
g = −3.

Solution:
grand = −iii, c = 8

Instance ii: y=mx+c form

Land the gradient and
y-intercept of the line
y = 7 − x.

Example 3: rearrange the equation when ten is the subject

State the gradient and
y-intercept of the line
10 = y + x.

Rearrange the equation to make



y
the discipline

Here we need to make
y
the subject field of the equation. We therefore need to make sure we isolate
y
on one side of the equals sign so that we express the equation in the form


y=mx+c
.

Example 4: changing the subject including a fraction

Country the gradient and
y-intercept of the line
2x = 6y − fifteen.

Rearrange the equation to make



y
the subject

Here we demand to make
y
the subject area of the equation. We therefore need to make sure we isolate
y
on one side of the equals sign so that we limited the equation in the form


y=mx+c
.

Example 5: changing the subject area including brackets

Land the gradient and
y-intercept of the line
3x = iv(y − five).

Rearrange the equation to make



y
the bailiwick

Hither we need to make
y
the subject of the equation. We therefore need to make sure we isolate
y
on i side of the equals sign and then that nosotros express the equation in the form


y=mx+c
.

Example six: irresolute the subject field including decimals

State the gradient and
y-intercept of the line

\[10=\frac{y+0.85}{0.2}.\]

Rearrange the equation to brand



y
the subject

Hither we need to brand
y
the subject of the equation. We therefore need to make sure we isolate
y
on one side of the equals sign so that we express the equation in the class



y=mx+c

.

Common misconceptions

• 
  Incorrect inverse operation
  

• 
  Stating the value of
  chiliad
  and
  c
  
  

• 
  Mixing up the gradient and the y-intercept
  

Have, for example, the equation
y = 10 + 3x. Here, the coefficient of
x
is
3
and the value of
y
when
x = 0
is
ten. This means that the slope is
three
and the
y-intercept is
10, not the other way around.

Still stuck?

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