Answer
$\frac{5}{6}$
Work Step by Step
The formula for the distance between the x intercept and y intercept is
$d = \sqrt ( (\frac{C}{A})^{2} + (\frac{C}{B})^{2} )$
for the equation Ax+ By = C
Given the equation 4x - 3y = 2 where A=4, B=-3 and C=2 so we substitute it into the equation
$d = \sqrt ( (\frac{C}{A})^{2} + (\frac{C}{B})^{2} )$
$d = \sqrt ( (\frac{2}{4})^{2} + (\frac{2}{-3})^{2} )$
We simplify the fractions by dividing the numerator by the denominator.
$d = \sqrt ( (\frac{1}{2})^{2} + (\frac{2}{-3})^{2} )$
$d = \sqrt ( \frac{1}{4})+ (\frac{4}{9}) $
We add the fractions together and get
$d = \sqrt ( \frac{25}{36}) $
*** Square root of 25 is 5 because 5 x 5 =25
*** Square root of 36 is 6 because 6 x 6 =36
$d = \frac{5}{6}$
