# What is the slope and intercept of 4x+y=1?

Jun 10, 2016

Slope: $\left(- 4\right)$
y-intercept$= 1 \textcolor{w h i t e}{\text{XXXX}}$x-intercept$= \frac{1}{4}$

#### Explanation:

For a linear equation in the general form:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{A} x + \textcolor{b l u e}{B} y = C$
the slope is $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

For the given equation $\textcolor{red}{4} x + y = 1 \Rightarrow \textcolor{red}{4} x + \textcolor{b l u e}{1} y = 1$
this becomes $m = - \frac{\textcolor{red}{4}}{\textcolor{b l u e}{1}}$

Alternately, you could convert the equation into slope-intercept form:
$\textcolor{w h i t e}{\text{XXX}} 4 x + y = 1 \Rightarrow y = \textcolor{g r e e n}{- 4} x + \textcolor{b r o w n}{1}$
with slope $\textcolor{g r e e n}{- 4}$ and y-intercept $\textcolor{b r o w n}{1}$
The advantage of this method is that it gives you the value of the y-intercept directly ($\textcolor{b r o w n}{1}$ in this case).

Otherwise the value of the y-intercept is the value of $y$ when $x = 0$
$\textcolor{w h i t e}{\text{XXX}} 4 x + y = 1$ with $x = 0$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 4 \left(0\right) + y = 1$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow y = 1$

The x-intercept can be found in a similar manner.
The value of the x-intercept is the value of $x$ when $y = 0$
$\textcolor{w h i t e}{\text{XXX}} 4 x + y = 1$ with $y = 0$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 4 x + 0 = 1$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = \frac{1}{4}$