line j: y = 2/3x + 1/2

A typical line in slope intercept form is

y = mx + b

where m is the slope and a is the y-intercept.

Two lines are parallel whenever their slopes (m1, m2) are identical.

Try to spot two lines with identical slopes and find the corresponding choice of answer.

It’s J and L

To determine which lines are parallel to each other, we need to compare their slopes.

The slope-intercept form of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept.

Comparing the slopes of the given lines, we find:

- Line j: y = (2/3)x + 1/2, slope = 2/3.
- Line k: y = (1/2)x + 2/3, slope = 1/2.
- Line l: y = (2/3)x + 3/2, slope = 2/3.
- Line m: y = (3/2)x + 1/2, slope = 3/2.

We can see that lines j and l both have a slope of 2/3, therefore they are parallel to each other.

So, the correct answer is A) j and l are parallel to each other.

To determine which lines are parallel to each other, we need to compare their slopes.

The slope-intercept form of a line is given by the equation y = mx + b, where m represents the slope of the line.

For line j: y = (2/3)x + 1/2, the slope is 2/3.
For line k: y = (1/2)x + 2/3, the slope is 1/2.
For line l: y = (2/3)x + 3/2, the slope is 2/3.
For line m: y = (3/2)x + 1/2, the slope is 3/2.

Now we compare the slopes:
Line j has a slope of 2/3, and line l has a slope of 2/3. Therefore, lines j and l are parallel to each other.

Line k has a slope of 1/2, and line l has a slope of 2/3. Therefore, lines k and l are not parallel to each other.

Line k has a slope of 1/2, and line m has a slope of 3/2. Therefore, lines k and m are not parallel to each other.

Based on the comparison of slopes, the lines that are parallel to each other are j and l. So the correct answer is A) j and l.