Question
Draw the graph of the following linear equations in two variables:
$\frac{\text{x}}{2}-\frac{\text{y}}{3}=2$
$\frac{\text{x}}{2}-\frac{\text{y}}{3}=2$
✓
Answer
We have,
$\frac{\text{x}}{2}-\frac{\text{y}}{3}=2$
$\Rightarrow\frac{3\text{x}-2\text{y}}{6}=2$
$\Rightarrow3\text{x}-2\text{y}=12$
$\Rightarrow3\text{x}=12+2\text{y}$
$\Rightarrow\text{x}=\frac{12+2\text{y}}{3}$
Putting y = -6, we get $\text{x}=\frac{12+2(-6)}{3}=0$
Putting y = -3, we get $\text{x}=\frac{12+2(-3)}{3}=2$
Thus, we have the following table giving two points on the line represented by the equation $\frac{\text{x}}{2}-\frac{\text{y}}{3}=2:$
Graph of the equation $\frac{\text{x}}{2}-\frac{\text{y}}{3}=2:$
$\frac{\text{x}}{2}-\frac{\text{y}}{3}=2$
$\Rightarrow\frac{3\text{x}-2\text{y}}{6}=2$
$\Rightarrow3\text{x}-2\text{y}=12$
$\Rightarrow3\text{x}=12+2\text{y}$
$\Rightarrow\text{x}=\frac{12+2\text{y}}{3}$
Putting y = -6, we get $\text{x}=\frac{12+2(-6)}{3}=0$
Putting y = -3, we get $\text{x}=\frac{12+2(-3)}{3}=2$
Thus, we have the following table giving two points on the line represented by the equation $\frac{\text{x}}{2}-\frac{\text{y}}{3}=2:$
Graph of the equation $\frac{\text{x}}{2}-\frac{\text{y}}{3}=2:$
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