y=mx+c Worksheets | Questions and Revision | MME

y=mx+c Worksheets, Questions and Revision

Level 4 Level 5
GCSE Maths Revision Cards

What you need to know

The equation of a straight line 

Any straight line graph can be described by the following equation:

\textcolor{limegreen}{y}=\textcolor{red}{m}\textcolor{limegreen}{x}+\textcolor{blue}{c}

\textcolor{red}{m} is the gradient 

\textcolor{blue}{c} is the y-intercept.‏ (the point where the line touches the y axis)

\textcolor{limegreen}{x} and \textcolor{limegreen}{y} are the coordinates the line passes through.

Make sure you are familiar with the following topics before continuing. 

 – Gradients straight line graphs revision

 – Rearranging formula 

Example 1: Finding y=mx+c

Find the equation of the straight line shown below.

So, we are looking for an equation of the form

\textcolor{limegreen}{y}=\textcolor{red}{m}\textcolor{limegreen}{x}+\textcolor{blue}{c}

First, finding \textcolor{blue}{c} the y-intercept – looking at the graph, we can see it touches the axis at -1, therefore we have \textcolor{blue}{c=-1}.

Then, to work out the gradient,

\text{Gradient } = \dfrac{\textcolor{red}{\text{change in }y}}{\textcolor{blue}{\text{change in }x}}

The triangle we have drawn has height 4 and width 2, so we get

m=\text{gradient}=\dfrac{\textcolor{red}{4}}{\textcolor{blue}{2}}=2

Therefore, we have that the equation of the straight line is

y=2x-1

Example 2

Find the equation of the line that passes through (-3, 1) and (2, -14).

Like in the last example, we want an equation of the form

\textcolor{limegreen}{y}=\textcolor{red}{m}\textcolor{limegreen}{x}+\textcolor{blue}{c}

Firstly, the gradient in the same way as before,

m=\text{gradient}=\dfrac{(-14)-1}{2-(-3)}=\dfrac{-15}{5}=-3

Now we know that m=-3, we know that our equation must take the form

y=-3x+c.

Finding \textcolor{blue}{c}.

We use the x and y valyues of one co-ordinate and plug them into the equation

(-3,1) = (x,y)

x = -3, y=1

Putting these into the equation we get

1=(-3)\times(-3)+c=9+c

Now solve for c

c=1-9=-8

Now we have all the components of a line equation, we can write the resulting equation as

y=-3x-8.

Example 3

Find the gradient and y-intercept of the line x+2y=14.

We want to rearrange this equation to make y the subject. So, subtracting x from both sides, we get

2y=-x+14

Then, dividing both sides by 2, we get

y=-\dfrac{1}{2}x+7

Therefore, the gradient -\dfrac{1}{2} and the y-intercept is 7.

Example Questions

We want an equation of the form

 

y=mx+c

 

So, we need to find the gradient, m, and y-intercept, c.

 

Firstly, looking at the graph we can see that the y-intercept is 2, so c=2.

 

Now, we will find the gradient by drawing a triangle underneath the line in question.

The triangle we have drawn has height 1 and width 3, so we get

 

m=\text{gradient}=\dfrac{1}{3}

 

Therefore, the equation of the line is

 

y=\dfrac{1}{3}x+2

We want an equation of the form

 

y=mx+c

 

So, we need to find the gradient, m, and y-intercept, c.

 

Firstly, we will find the gradient by the dividing the difference in the y coordinates by the difference in the x coordinates:

 

m=\text{gradient}=\dfrac{-6-34}{-3-2}=\dfrac{-40}{-5}=8

 

Therefore, the equation of the line is

 

y=8x+c

 

Then, to find c we will substitute one pair of coordinates that the line passes through into the equation and rearrange. Here, we’ll pick (2, 34). Subbing this in, we get

 

34=8\times2+c=16+c

 

Subtracting 16 from both sides, we get

 

c=34-16=18

 

Therefore, the equation of the line is

 

y=8x+18.

Worksheets and Exam Questions

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