# How do you graph using slope and intercept of 2x+y=8?

Oct 16, 2017

(see below for method used in generating this graph)

#### Explanation:

The slope of a line in the form $A x + B y = C$ is $\left(- \frac{A}{B}\right)$

The y-intercept is the value of $y$ when $x = 0$

In this case $2 x + y = 8$
$\textcolor{w h i t e}{\text{XXX}}$ slope $= - \frac{2}{1} = - 2$
and
$\textcolor{w h i t e}{\text{XXX}}$ the $y$ intercept is $8$ (since $2 \times 0 + y = 8 \rightarrow y = 8$)

Based on the $y$-intercept we know that one point on the line is at $\left(x , y\right) = \left(0 , 8\right)$

The slope of $\left(- 2\right)$ tells us that for every unit increment (i.e. $+ 1$) of the $x$ value, the $y$ value changes by $\left(- 2\right)$

So we can build a table of a few Sample points:
color(white)("XXX"){:(ul(x),color(white)("xxx"),ul(y)),(0,,8),(1,,6),(2,,4),(3,,2) :}

Plotting these coordinates on the Cartesian plane and drawing a straight line through them should give a graph that looks like the Answer above.