What is the distance between y = 3x + 9 and y = 3x - 4?

  A.  4.11 units

Step-by-step explanation:

It can be convenient to put one of these equations into general form, then use the formula for the distance from a point to a line.

In general form, the first equation is ...

  3x -y +9 = 0

So, the distance from a point to that line is ...

  ax +by +c = 0 . . . . . . equation of a line

  d = |ax +by +c|/√(a^2+b^2) . . . corresponding distance formula

  d = |3x -y +9|/√(3^2 +(-1)^2)

Using the y-intercept of the other line as the point of interest, we find its distance to the first line to be ...

  d = |3(0) -(-4)+9|/√10 = 13/√10 ≈ 4.11

The distance between the lines is about 4.11 units.

_____

Unless the lines are vertical or horizontal, you know the distance will be less than the difference between the x- or y- intercepts. Here, the y-intercepts are separated by 9-(-4) = 13 units. The x-intercepts are -3 and 4/3, so are separated by 4 1/3 units. Any answer choice larger than 4.33 cannot be correct.

you need to add a picture

step-by-step explanation:

for exempl this   system of equations   y = x - 3

                                                                y = 2x - 5

look   the line : y = x -3     ( red)

                            the line : y = 2x -5 ( bleus)