Hi Melissa M

To help I would recommend that you set all your given lines in Slope Intercept Form, this will help you to easily see what your slope should be based on the criteria. Parallel lines have exactly the same slope

**a.**

x - 5y = 15

Solve this for y to get it in Slope Intercept Form

y = mx + b

-5y = - x + 15

y = (1/5)x - 3

In this form the slope, the coefficient of x becomes obvious, m = 1/5

So of the slope of the parallel line is 1/5

y = (1/5) + b

Next we use the coordinates of the point given (5, -1) to solve for b

-1 = (1/5)*5 + b

-1 = 1 + b

-1 -1 = b

-2 =b

Now just plug this into the equation of the Parallel for question a

y = (1/5)x - 2

You can graph both lines to confirm that they are parallel and pass through the given point at Desmos.com

With that in mind the rule for Perpendicular Lines says that they have inverse slopes of opposite sign, we need this information for line b they we can use the same process

**b**

3x - y = 4

In Slope Intercept Form

-y = -3x + 4

y = 3x - 4

Again the coefficient of x, the slope is 3, so the slop of the Perpendicular line is the negative inverse of 3 which is (-1/3)

We can start building the equation

y = (-1/3) + b

Plug in the coordinates given (6, 2) to solve for b

2 = (-1/3)*6 + b

2 = -2 + b

2 + 2 = b

4 = b

So we can plug this value into our Perpendicular Line

y = (-1/3)x + 4

Again you can graph everything at Desmos.com

I hope your find this useful