+107 Find the distance between the x-intercept and the y-intercept of the graph of the equation \($3x - 7y = 21$ \).
+781 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 \(\boxed{\sqrt{58}}\).
