Start by re-arranging the given equation into slope-intercept form.

Recall that perpendicular lines have slopes that are negative reciprocals of each other. This means that the line that is perpendicular to the given one has a slope of .

 is the only line with that slope.

If the slope of a line is given, the slope of a line perpendicular to it is the additive inverse of the reciprocal of the slope of the first line. Thus, the slope sought is 

.

Start by converting the standard form of the linear equation to the slope-intercept form.

Recall that lines that are perpendicular must have slopes that are negative reciprocals.

Thus the slope of a line that is perpendicular to the given one must be . The line with the equation  is the only one that has the correct slope.

Recall that perpendicular lines have slopes that are negative reciprocals of each other. Thus, rewrite the given equation in slope-intercept form to find its slope.

Since the given equation has a slope of , the line perpendicular to it must have a slope of .  is the only line with the correct slope.

Recall that parallel lines must have the same slope. Start by putting the given equation into slope-intercept form.

Since the given equation has a slope of , the only line with the same slope is .

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.