How do you graph the line -4x - 16y = 4?

Mar 29, 2016

See explanation

Explanation:

The easiest way is to manipulate the equation into the form of

$y = m x + c$

The assign different values to x from which you can then calculate the corresponding value for y. For a straight line graph you only need two points that you can join up and extend to give the graph plot. How ever, 3 points are better as it increases the chance of showing up any error. All 3 points should line up.
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$\textcolor{b l u e}{\text{Solving your question}}$

Given;$\text{ } - 4 x - 16 h = 4$

To make the $y$ term positive multiply everything by (-1) giving

$\textcolor{b r o w n}{+ 4 x + 16 y = - 4}$

Subtract #color(blue)(4x) from both sides

$\textcolor{b r o w n}{+ 4 x \textcolor{b l u e}{- 4 x} + 16 y = - 4 \textcolor{b l u e}{- 4 x}}$

$0 + 16 y = - 4 x - 4$

Divide both sides by 16

$\frac{16}{16} \times y = - \frac{4}{16} x - \frac{4}{16}$

But $\frac{16}{16} = 1$ and $\frac{4}{16} = \frac{1}{4}$giving

$y = - \frac{1}{4} x - \frac{1}{4}$

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