# How do you graph the line  2x - 5y=10?

Apr 10, 2016

Transpose (manipulate) the equation as follows:

Add $\textcolor{b l u e}{5 y}$ to both sides

$\textcolor{b r o w n}{2 x - 5 y \textcolor{b l u e}{+ 5 y} = 10 \textcolor{b l u e}{+ 5 y}} \text{ "->" } 2 x + 0 = 10 + 5 y$

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Subtract $\textcolor{b l u e}{10}$ from both sides

$\textcolor{b r o w n}{2 x \textcolor{b l u e}{- 10} = 10 \textcolor{b l u e}{- 10} + 5 y} \text{ "->" } 2 x - 10 = 0 + 5 y$

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Divide both sides by $\textcolor{b l u e}{5}$

color(brown)( (2x)/(color(blue)(5)) -10/(color(blue)(5)) = 5/(color(blue)(5)) xx x

But $\frac{5}{5} = 1$

$\textcolor{b l u e}{y = \frac{2}{5} x - 2} \text{ }$This is standard form of the equation
$\textcolor{red}{\text{=================================}}$

The line crosses the y-axis ( y_("intercept" ) when $x = 0$

so ${y}_{\text{intercept}} = \frac{2}{5} \left(0\right) - 2 = - 2$

So one point is:$\text{ } \left(x , y\right) \to \left(0 , - 2\right)$

$\textcolor{red}{\text{Mark that point on the graph}}$
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The line crosses the x-axis ( ${x}_{\text{intercept}}$ ) at $y = 0$

$0 = \frac{2}{5} x - 2$

$\implies 2 \times \frac{5}{2} = x = 5$

So the other point is:$\text{ } \left(x , y\right) \to \left(5 , 0\right)$
$\textcolor{red}{\text{Mark that point on the graph}}$
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$\textcolor{b l u e}{\text{Draw a line through both these points and that is your graph.}}$