Find, to four significant digits, the distance between the graphs of 2x-3y+4=0 and 2x-3y+15=0.

In analytical geometry, we can find the linear distance between two parallel lines by determining the coefficients of the variables and the constants. The general equation for a linear equation is: Ax + By = C.

Line 1: 2x - 3y = - 4

Line 2: 2x - 3y = - 15

In this case, A=2 and B=-3. The constants are C₁ = - 4 and C₂ = - 15. The distance follows this formula:

d = |C₁ - C₂| / (√ (A²+B²)

d = |⁻4 - ⁻15| / (√ (2²+⁻3²)

d = 3.051 units