y=mx+c

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).

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).

Step 1: Finding the gradient,

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

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.