How do you graph 6x+4y=12 using intercepts?

Mar 22, 2017

See explanation

Explanation:

Given:$\text{ } 6 x + 4 y = 12$

Believe it or not, if you divide both sides by 2 and plot you will find that both equations produce exactly the same plot.

Divide both sides by 2

$3 x + 2 y = 6$

You could manipulate this into the form $y = m x + c$ but you do not need to.
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We know that the x-axis crosses the y-axis at $x = 0$ so to determine the y-intercept set $x = 0$

$3 x + 2 y = 6 \text{ "->" } 3 \left(0\right) + 2 y = 6$
$\text{ } 2 y = 6$
$\text{ } y = 3$

${y}_{\text{intercept}} = 3$
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We know that the y-axis crosses the x-axis at $y = 0$ so to determine the x-intercept set $y = 0$

$3 x + 2 y = 6 \text{ "->" } 3 x + 2 \left(0\right) = 6$
$\text{ } 3 x = 6$
$\text{ } x = 2$

${x}_{\text{intercept}} = 2$
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Mark your points and draw a straight line through them. 