# How do you find the x and y intercept of 3x+2y=6?

Apr 5, 2017

${y}_{\text{intercept}} = 3 \to \left(x , y\right) = \left(0 , 3\right)$

${x}_{\text{intercept}} = 2 \to \left(x , y\right) = \left(2 , 0\right)$

#### Explanation:

Subtract $3 x$ from both sides giving:

$2 y = - 3 x + 6$

Divide each side by 2

$y = - \frac{3}{2} x + 3$
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The y-intercept is at $x = 0$ giving:

$y = - \frac{3}{2} \left(0\right) + 3$

${y}_{\text{intercept}} = 3 \to \left(x , y\right) = \left(0 , 3\right)$
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The x-intercept is at $y = 0$ giving:

$0 = - \frac{3}{2} x + 3$

$\frac{3}{2} x = 3$

$x = \frac{2}{3} \times 3 = 2$

${x}_{\text{intercept}} = 2 \to \left(x , y\right) = \left(2 , 0\right)$