Which is the distance between parallel lines with the equations 3x-5y=1 and 3x-5y=-3

The distance between parallel lines is

Step-by-step explanation:

we have

-----> equation A

-----> equation B

Line A and Line B are parallel lines, because their slopes are equal

Step 1

Find the slope of the given lines

isolate the variable y in the equation A

The slope is

Step 2

Find the slope of the perpendicular line to the given lines

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

we have

-----> given lines

substitute

Step 3

Find the equation of the perpendicular line that pass though the origin

 with the slope   and the point (0,0) Find the equation of the line

Step 4

Using a graphing tool

Graph the two parallel lines and the perpendicular line

The intersection points are

and  

see the attached figure

we know that

the distance between the points A and B is the distance between parallel lines

the formula to calculate the distance between two points is equal to

substitute the values

c.

step-by-step explanation: