Answer:
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.
