# How do you write an equation of a line given y-intercept -8 and slope 3?

Jan 21, 2016

$y = 3 x - 8$

I have given a detailed explanation about how it all works.

#### Explanation:

Consider the standard form of the equation for a strait line:

$y = m x + c$........................................(1)

Where
$m \to$ is the gradient (slope)
$c \to \textcolor{w h i t e}{.}$ is a constant (its value does not change)
$x \to \textcolor{w h i t e}{.}$ is a variable (can take on any value you chose)
$y \to \textcolor{w h i t e}{.}$ is the dependant variable (the answer)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{The gradient (slope)}}$
$\textcolor{g r e e n}{\text{We are told that the gradient (slope) is 3.}}$

so equation (1) becomes:

$\textcolor{b l u e}{y = \textcolor{g r e e n}{3} x + c}$

$\textcolor{red}{\text{This is what the graph would look like if there was no } c}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{To find the value of } \textcolor{g r e e n}{c}}$

Suppose we put the value of the y-intercept (given as -8) into the equation were $c$ is. So equation (1) becomes

$\textcolor{b l u e}{y = 3 x \textcolor{g r e e n}{- 8}}$

$\textcolor{red}{\text{This time the graph look like:}}$

So for the equation of a strait line the $c$ in the equation is the y-intercept.

Change the value of c moves the plotted line up or down

Imagine for a moment that $c = 2$ then the line would cross the y-axis at y=2.

If $c = - 3$ then the y-intercept would be -3