# How do you graph using the intercepts for -4x-2y=14?

Oct 4, 2016

See explanation

#### Explanation:

This is a straight line equation.

$\textcolor{b l u e}{\text{Using first principles method}}$

Given:$\text{ } - 4 x - 2 y = 14$

Add $2 y$ to both sides

$14 + 2 y = - 4 x$

Subtract 14 from both sides

$2 y = - 4 x - 14$

Divide both sides by 2

$y = - \frac{4}{2} x - \frac{14}{2}$

$\textcolor{b l u e}{y = - 2 x - 7}$
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$\textcolor{b l u e}{\text{Using shortcut method}}$
$\textcolor{b r o w n}{\text{It takes a lot more lines to explain than to do it!}}$

Move $- 2 y$ to the other side of = and change its sign
$- 4 x = 14 + 2 y$

Move the 14 to the other side of = and change its sign

$- 4 x - 14 = 2 y$

Write as:
$2 y = - 4 x - 14$

Move the 2 from $2 y$ to the other side of the = and change it from multiply to divide (reverse its action)
$y = - \frac{4}{2} x - \frac{14}{2}$

$\textcolor{b l u e}{y = - 2 x - 7}$..................Equation(1)
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The intercepts are at when $x = 0$ and $y = 0$

$\textcolor{b r o w n}{\text{Set "x=0" so Equation(1) becomes:}}$

$y = - 2 \left(0\right) - 7$
y=-7 ->" "color(blue)((x,y)=(0,-7) larr" y-intercept")

$\textcolor{b r o w n}{\text{Set "y=0" so Equation(1) becomes:}}$

$0 = - 2 x - 7$

$+ 2 x = - 7$

x=-7/2->" "color(blue)((x,y)=(-7/2,0)larr" x-intercept")#
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Mark your two points and draw a straight line through them