The first equation is written in standard form: . In this format, the slope is equal to .

The second equation is written in slope-intercept form: . The slope is given by the value of .

Because the slopes of both lines are equal, the lines must be parallel.

Parallel lines have the same slope. To find the slope of a given equation, it is necessary to convert it to slope-intercept form.

Subtract the from both sides.

Divide by .

Understanding slope-intercepts form, we can see that the slope is .

We can convert each answer choice to slope-intercept form to detrmine which has a slope matching the equation in the question.

This equation has the same slope, and is therefore parallel.

Two lines can only be parallel if they have identical slopes. In this case, the slope is , which is equal to . The only line that has the same slope is

so that is the correct answer. Take note that the  value does not matter when determining whether two lines are parallel, unless the values are the same, in which case the lines would be identical and not parallel.

We are given

and we compare it to the general formula of a straight line

where  is the slope and is the y-intercept.  In our case, . Know that in order for another function to be parallel, it has to have the same slope.  Therefore, we pick an answer choice that has the slope of . It turns out that the answer choice is

Parallel lines need to have slopes that are equal.  For the line , the slope is 3, since this is the coefficient attached to the x-variable.  For the line , the slope is 4.  Because these slopes are not equal, the lines are not parallel.

For two lines to be parallel, they must have the same slope. So, we are looking for a line with a slope of . However, it's difficult to tell what the slopes of the answer choices are because they are not in slope-intercept form. Luckily, it's easy to convert them.

Take the answer choice . Subtracting  from both sides gives 

which can be simplified to 

This is our answer! To be safe, the other choices can be rewritten in slope-intercept form as well, upon which it becomes clear that none of them are parallel.

Parallel lines have identical slopes. The slope of the given line is 8, so the slope of the parallel line must also be 8. The only other line with a slope of 8 is 

.

For lines to be parallel, they need to have the same slope. In the form  we know  is the slope of the function. Therefore,  has .

Now looking at the possible answer choices we see that, 

can be written in slope-intercept form by dividing both sides by two, which equals

.

We can see that this equation also has slope , the same as the given equation. Thus these two lines are parallel.

To find out if lines are parallel or perpendicular you must look at the slopes of both lines. If they have the same slope then they are parallel and go in the same direction. If they have opposite slopes, then they are perpendicular and go in opposite directions and will eventually cross eachother at a right angle.

We have the following equations:

and

They are written in slope-intercept form:

In this form,  is the slope. The slopes are both   in our equations; therefore, the lines are parallel.

Parallel lines never cross nor do they diverge. They climb/descend at the same rate. What determines the "steepness" of a line? The slope does. In order for two lines to remain the same distance from each other (to be parallel) for their length , they must have the same rise-over-run (slope).

So for subject A whose HR increases at , the steepness of this person's heart rate's increase is the slope 1/5. Any other person whose heart rate increases by the same rate per minute (the slope) will have a HR that never exceeds or diverges (graphically, in the sense of the two lines) from the HR of subject A.

Subject B  is the only person who HR line increases with same slope and thus remains the same distance from that of Subject A .