Answer:
To find the distance between parallel lines, you can use the formula:
distance = |(c2 - c1)| / sqrt(a^2 + b^2)
Where the lines are represented in the form ax + by + c1 = 0 and ax + by + c2 = 0.
For the given equations:
Line 1: y = 3x + 4
Line 2: y = 3x - 5
We can rewrite the equations in the standard form:
Line 1: 3x - y + 4 = 0
Line 2: 3x - y + 5 = 0
Comparing the coefficients, we have:
a = 3
b = -1
c1 = 4
c2 = 5
Now we can calculate the distance:
distance = |(c2 - c1)| / sqrt(a^2 + b^2)
= |(5 - 4)| / sqrt(3^2 + (-1)^2)
= 1 / sqrt(9 + 1)
= 1 / sqrt(10)
≈ 0.316227766
Rounding the answer to the nearest hundredth, the distance between the parallel lines y = 3x + 4 and y = 3x - 5 is approximately 0.32
I hope that helped!!