The Linear Equation:

The given linear equation is 2yx = 7. To graph this equation, we need to rearrange it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

To rearrange the equation, we isolate y by dividing both sides of the equation by 2x:

2yx = 7
y = 7/(2x)

Now the equation is in slope-intercept form.

Graphing the Equation:

To graph the equation, we can choose different values for x and substitute them into the equation to find the corresponding y-values. Let's choose x-values of -2, -1, 0, 1, and 2:

When x = -2:
y = 7/(2*(-2)) = -7/4

When x = -1:
y = 7/(2*(-1)) = -7/2

When x = 0:
y = 7/(2*0) = undefined

When x = 1:
y = 7/(2*1) = 7/2

When x = 2:
y = 7/(2*2) = 7/4

Now we have five points: (-2, -7/4), (-1, -7/2), (0, undefined), (1, 7/2), and (2, 7/4).

Plotting the Points:
To plot the points, we will use a graph paper or a coordinate plane. The x-axis represents the horizontal values, and the y-axis represents the vertical values.

Plot the points (-2, -7/4), (-1, -7/2), (1, 7/2), and (2, 7/4) on the graph. However, since the point (0, undefined) is not defined, we cannot plot it on the graph.

Determining if (3, 2) Lies on the Line:

To check if the point (3, 2) lies on the line, we substitute x = 3 and y = 2 into the equation y = 7/(2x):

y = 7/(2*3) = 7/6

Therefore, when x = 3, y = 7/6, not 2. Hence, the point (3, 2) does not lie on the line represented by the equation 2yx = 7.

Conclusion:

The graph of the linear equation 2yx = 7 consists of the points (-2, -7/4), (-1, -7/2), (1, 7/2), and (2, 7/4). The point (3, 2) does not lie on this line.