Which of the following lines is perpendicular to the line below?

Perpendicular lines have slopes which are the opposite signed reciprocal of eachother.

What this means is that to find perpendicular slopes, we need to change the sign of our original slope, and then flip the numerator and the denominator. 

You might be thinking, but what is the numerator and what is the denominator of a whole number? 

Well, we can picture any whole number as having a denominator of 1. This means that we can get our reciprocal via the following.

We're almost there, by we also need to change the sign:

So, our answer must have a slope of one-fourteenth.

Which of the following lines is parallel to a line having a slope of  ?

For lines to be parallel, the slopes must be equal. That is the only way for the two lines to continuously run without ever crossing. 

So, we should look for a line with a slope of 

At first glance, there are not options. However, begin by eliminating any options which are already solved for y, which do not have the right slope.

So,

       and 

can be eliminated...

This leaves us with two options. For each option, divide both sides by the coefficient in front of the y, and simplify.

Now, does 55 over 14 equal 5 over 4? No, it is more like 3.9 than 1.25

This leaves us with our final option:

If we simplify we see that this should indeed be parallel.

Recall that perpendicular slopes are opposite and reciprocal.

So to get the slope of the blue line, all we need to do it to switch the sign on the green line and "flip-flop" the value

Green slope: 

Blue slope: 

Now all we need is the y-intercept, which we can tell by looking at the graph. We can see that when x=0, y=-1. So our y-intercept is =-1.

This gives us our final answer of

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in  form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations. 

The equation of the graphed line is . Since it is already in  form, we can quickly deduce that the slope is  Therefore, another line that also has a slope of  will be parallel to it. The only option is . The y-intercept value does not matter. 

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in  form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations. 

The equation of the graphed line is . Since it is already in  form, we can quickly deduce that the slope is  Therefore, aline that has a slope of  will be perpendicular to it. The only option is . The y-intercept value does not matter. 

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in  form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations. 

For this problem, the first step is to rewrite the graphed equation so it is in  form. Just keep in mind that what you do to one side, you must do to the other. 

Now we know that the slope of the graphed equation is . This means that for another line to be parallel, the second line must also have a slope of . 

The only provided option is . The y-intercept does not matter.

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in  form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations. 

For this problem, the first step is to rewrite the graphed equation so it is in  form. Just keep in mind that what you do to one side, you must do to the other. 

Now we know that the slope of the graphed equation is . This means that for another line to be perpendicular, the second line must have a slope of . 

The only provided option is . The y-intercept does not matter.

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in  form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations. 

For this problem, the first step is to rewrite the graphed equation so it is in  form. Just keep in mind that what you do to one side, you must do to the other. 

Now we know that the slope of the graphed equation is . This means that for another line to be parallel, the second line must  have the same slope.

The only provided option is . The y-intercept does not matter.

Use the midpoint formula:

Repeated application of the midpoint formula  yields the following:

Since  is the midpoint of , substitute the coordinates of  for  and , set equal to the coordinates of , and solve as follows:

 is the point .

We can find the coordinates of  similarly using those of  and :

 is the point