# What is the slope and intercept for y=1/4x and how would you graph it?

Oct 15, 2015

Slope: $\frac{1}{4}$
y-intercept: $0$
(see below for graph)

#### Explanation:

The slope-intercept form of a linear equation is
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$
$\textcolor{w h i t e}{\text{XXXXXX}}$where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept.

$y = \frac{1}{4} x \Leftrightarrow y = \textcolor{red}{\frac{1}{4}} x + \textcolor{b l u e}{0}$

$\rightarrow$ slope $= \textcolor{red}{\frac{1}{4}}$ and y-intercept $= 0$

Since the y-intercept is $0$
the line goes through the point $\left(0 , 0\right)$
and substituting some multiple of $4$ (e.g. $8$) for $x$we can easily determine a second point (in this case $\left(8 , 2\right)$)

Plot these two points on the Cartesian plane and draw a line through them for the required graph.
graph{(y-x/4)(x^2+y^2-0.01)((x-8)^2+(y-2)^2-0.01)=0 [-1.885, 13.915, -3.42, 4.48]}