2 Answers

Jwarchol · Answer 1 · 2020-01-22T16:28:48+0000

Question 1:

For this case we have the following function:

$y = - \frac {3} {2} x + 6$

We want to find a parallel line that passes through the point
$(x_ {0}, y_ {0}) = (2, -1)$

If the lines are parallel, then the slopes are equal
$m_ {1} = m_ {2} = - \frac {3} {2}$

Therefore, the equation of the line is given by:

$y-y_ {0} = m_ {2} (x-x_ {0})$

Substituting values we have:

$y - (- 1) = - \frac {3} {2} (x-2)\\y + 1 = - \frac {3} {2} (x-2)$

Rewriting the equation we have:

$y = - \frac {3} {2} x + 3-1\\y = - \frac {3} {2} x + 2$

Answer:

$y = - \frac {3} {2} x + 2$

Option C

Question 2:

For this case we have the following equation:

x = -3

We want to find a parallel line that passes through the point
$(x_ {0}, y_ {0}) = (4,2)$

If the straight lines are parallel, then the slopes are equal.

In this case, the slope is not defined because the equation of the given line is vertical.

Therefore, the equation of the parallel line is of the form:

x = k

As the line passes through the point
$(x_ {0}, y_ {0}) = (4,2)$ , then the equation of the line is given by:

x = 4

Answer:

Option D

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