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 .

Parallel lines are lines that never intersect. This is a result of having the same slope, creating equal distance between points on the two lines.

The student would run through the sets of equations putting them into form to isolate , the variable representing the slope of the line.

The only set of equations with the same slope is

--

For two lines to be parallel, they must have the same slope.

Lines can be written in the slope-intercept form:

In this equation,  equals the slope and  represents the y-intercept.

The slope of the given line is:

There is only one line with a slope of .

For two lines to be parallel, they must have the same slope.

Lines can be written in the slope-intercept form:

In this equation,  equals the slope and  represents the y-intercept.

The slope of the given line is:

There is only one line with a slope of .

For two lines to be parallel, they must have the same slope.

Lines can be written in the slope-intercept form:

In this equation,  equals the slope and  represents the y-intercept.

The slope of the given line is:

There is only one line with a slope of .

For two lines to be parallel, they must have the same slope.

Lines can be written in the slope-intercept form:

In this equation,  equals the slope and  represents the y-intercept.

The slope of the given line is:

There is only one line with a slope of .

For two lines to be parallel, they must have the same slope.

Lines can be written in the slope-intercept form:

In this equation,  equals the slope and  represents the y-intercept.

The slope of the given line is:

There is only one line with a slope of .

For two lines to be parallel, they must have the same slope.

Lines can be written in the slope-intercept form:

In this equation,  equals the slope and  represents the y-intercept.

The slope of the given line is:

There is only one line with a slope of .