Question

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

Answer 1

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