Will mark 1.) write an equation for the line that is parallel to the given line and passes through the given point. y = 2x + 4; (3, 8) a.) y = 2x + 2 b.) y = 2x + 6 c.) y = -2x + 6 d.) y = -1/2x + 2 2.) tell whether the lines for each pair of equations are parallel, perpendicular, or neither. y = -2x + 4 -5x + 10y = 5 a.) parallel b.) perpendicular c.) neither 3.) tell whether the lines for each pair of equations are parallel, perpendicular, or neither. y = -1/4x + 8 -2x + 8y = 4 a.) parallel b.) perpendicular c.) neither 4.) write the equation for the line that is perpendicular to the given line and passes through the given point. y - 4 = 5/2 (x + 3); (-7, 8) a.) y - 8 = -2/5 (x - 7) b.) y - 8 = 2/5 (x - 7) c.) y - 8 = -2/5 (x + 7) d.) y - 8 = 2/5 (x + 7)

1. A parallel line would have the same slope as this line, 2x, so we already know that either A or B will be the answer.

So, we plug in the coordinates (3,8) to see which one works: for A, the new equation would be 8=2(3)+2, which become 8=6+2, and then 8=8.

Since this is true, the answer would be A: y= 2x + 2.

2. We have to turn the equation -5x+10y=5 in to a y= equation so it’s easier to compare.

First, we add 5x to both sides to get 10y by itself: 10y = 5x + 5.
Now we divide both sides by 10 to get y by itself: y= 0.5x + 5.

In order for the lines to be perpendicular, the slopes must be opposite reciprocals of each other. The opposite of -2 is 2 and the reciprocal of 2 is 1/2, or 0.5, so these lines are B: perpendicular.

3. We must do the same thing with the second equation as we did with last question.

First, we add 2x to both sides to get 8y by itself: 8y = 2x - 4.
Now we divide both sides by 8 to get y by itself: y= 0.25x - 0.5.

As mentioned before, the slopes must be opposite and reciprocal of each other to be perpendicular. They are opposites, but since 0.25 is the same as the fraction 1/4, they are not reciprocals and so are not perpendicular.

Since they are opposites, they are also not parallel, so these lines would be C: neither.

4. As we’ve already established, a perpendicular line has an opposite and reciprocal slope of the original line. The opposite and reciprocal of 5/2 is -2/5, which means that either A or C is the answer.

In the form that these equation are in, the x-value is shown in parentheses as (x - h), with h being the x-value. This means that the h value will be the opposite in the equation of what it was in the original coordinates. The original x-coordinate is -7, so it will appear as (x + 7) in the equation.

Therefore, C: y-8= -2/5(x+7) would be the correct answer.