Question

The question is in the picture

Answer 1

For this case we have by definition that if two lines are parallel, then their slopes are equal.

We have the following line:

`-2x + 4y = 8`

Manipulating algebraically we have:

`4y = 8 + 2x`

`y = \frac {2x} {4} + \frac {8} {4}\\y = \frac {1} {2} x + 2`

Thus, the slope is
`m = \frac {1} {2}`

Then, a parallel line will be of the form:

`y = \frac {1} {2} x + b`

We find the cut point "b" replacing the point:

`-1 = \frac {1} {2} (- 5) + b\\-1 = - \frac {5} {2} + b\\b = -1 + \frac {5} {2}\\b = \frac {-2 + 5} {2}\\b = \frac {3} {2}`

Finally, the line is:

`y = \frac {1} {2} x + \frac {3} {2}`

ANswer:

Option A