# How do you graph using the intercepts for 8x+6y=1?

Jan 28, 2016

Plot the two points for the intercepts and draw a line through them.

#### Explanation:

y-intercept
$\textcolor{w h i t e}{\text{XXX}}$the value of $y$ when $x = 0$
$\textcolor{w h i t e}{\text{XXXXX}} 8 \cdot 0 + 6 y = 1$
$\textcolor{w h i t e}{\text{XXXXX}} \rightarrow y = \frac{1}{6}$
$\textcolor{w h i t e}{\text{XXX}}$the y-intercept gives us the point $\left(0 , \frac{1}{6}\right)$

x-intercept
$\textcolor{w h i t e}{\text{XXX}}$the value of $x$ when $y = 0$
$\textcolor{w h i t e}{\text{XXXXX}} 8 x + 6 \cdot 0 = 1$
$\textcolor{w h i t e}{\text{XXXXX}} \rightarrow x = \frac{1}{8}$
$\textcolor{w h i t e}{\text{XXX}}$the x-intercept gives us the point $\left(\frac{1}{8} , 0\right)$

Plot these two points (you will want to use a magnified graphing grid):
graph{((x-1/8)^2+y^2-0.0001)(x^2+(y-1/6)^2-0.0001)=0 [-0.7216, 0.9644, -0.3086, 0.5344]}

Draw a straight line through these two points:
graph{(8x+6y-1)((x-1/8)^2+y^2-0.0001)(x^2+(y-1/6)^2-0.0001)=0 [-0.7216, 0.9644, -0.3086, 0.5344]}