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

# y=mx+c Worksheets, Questions and Revision

Level 4-5

## The Equation of a Straight Line ($y=mx+c$)

A straight line graph will always have an equation in the form $y=mx+c$. You need to be able to work out the equation of a straight line from a graph, as well as manipulate the equation itself.

There are 3 key skills you need to learn involving the equation of a straight line.

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

## The straight line equation

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

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

where $\textcolor{red}x$ and $\textcolor{red}y$ are the coordinates the line passes through, $\textcolor{limegreen}m$ is the gradient and $\textcolor{blue}c$ is the $y$-intercept (the $y$-coordinate where the line crosses the $y$ axis).

KS3 Level 4-5

## Test your skills with online exams on the MME Revision Platform

##### 5 Question Types

Our platform contains 5 question types: simple, multiple choice, multiple answers, fraction and image based questions. More question types are coming soon.

##### Written Solutions

Get written solutions for every single exam question, detailing exactly how to approach and answer each one, no matter the difficulty or topic.

Every exam attempt is stored against your unique student profile, meaning you can view all previous exam and question attempts to track your progress over time.

KS3 Level 4-5

## Skill 1:Finding the Equation of a Straight Line

We need to be able to find the equation of a straight line from the graph.

Example: Find the equation of the straight line graph below Step 1: Find $\textcolor{blue}{c}$

We are looking for an equation of the form,

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

We know $\textcolor{blue}{c} = y$-intercept. Looking at the graph, we can see it crosses the axis at $- 1$, therefore we have $\textcolor{blue}{c=-1}$. Step 2: Find the gradient ($\textcolor{limegreen}{m}$)

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,

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

Therefore, the equation of the straight line is,

$y=\textcolor{limegreen}{2}x\textcolor{blue}{-1}$

KS3 Level 4-5
KS3 Level 4-5

## Skill 2: Finding the Equation of a Line Through Two Points

Finding the equation of a straight line between two points is an important skill.

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

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

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

$y=-3x+c$

Step 2: Substitute the $x$ and $y$ values of one co-ordinate, say $x = -3, y=1$, into the equation,

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

Step 3: Rearrange to solve for $c$,

$c=1-9=-8$

Step 4: Now we have all the components of the equation of a line, we can write the resulting equation as,

$y=-3x-8$

KS3 Level 4-5
KS3 Level 4-5

## Skill 3:Rearranging Equations into the form $y=mx+c$

It is often necessary to rearrange the equation of a line to get it in the form $y=mx+c$. This is essential for finding the gradient and $y$-intercept.

Example: 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 is $-\dfrac{1}{2}$ and the $y$-intercept is $7$.

KS3 Level 4-5

## GCSE Maths Revision Cards

(252 Reviews) £8.99

### 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 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

$y=8x+18$.

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 $- 1$, so $c=-1$.

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

$m=\text{gradient}=\dfrac{3}{2}$ Therefore, the equation of the line is

$y=\dfrac{3}{2}x-1$

### Worksheets and Exam Questions

#### (NEW) y=mx+c Exam Style Questions - MME

Level 4-5 New Official MME