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Find the distance between the x-intercept and the y-intercept of the graph of the equation \($3x - 7y = 21$ \).

 Jun 23, 2020
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We write the equation in 3x-7y=21 first. 

3x-7y=21

7y=3x-21

y=3/7x-3

 

To find the x-intercept, we plug in the value 0 for y.

 

0=3/7x-3

3/7x=3

x=7

 

To find the y-intercept, we plug in the value 0 for x.

 

y=3/7(0)-3

y= -3

 

The x-intercept is (7,0) and the y-intercept (0, -3).

To find the distance, we plug the points into the distance formula.

 

\(\sqrt{(7-0)^2+0-(-3)^2}\\ \sqrt{49+7}\\ \sqrt{58}\\ \)

 

Therefore the distance between the x and y intercept is \(\boxed{\sqrt{58}}\).

 Jun 24, 2020

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