Question

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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