Question

Line BC is represented by 3x + 2y = 8. Line AD is represented by –3x – 2y = 6. What is the relationship of line BC to line AD? Explain how the sum of the equations demonstrates this relationship.

Answer 1

The correct answer for this question is this one:

The equations are:
BC: 3x + 2y = 8.
The slope of line BC is -3/2
y = -3/2 + 4

AD: –3x – 2y = 6.
The slope of line AD is -3/2
y = -3/2x - 3
So the relationship of the two lines is parallel lines.

Hope this helps answer your question and have a nice day ahead.

Answer 2

The line BC and line AD are parallel to each other and this can be determine by first determine the slope of both the lines by using slope intercept form.

Given :

• Line BC is represented by 3x + 2y = 8.
• Line AD is represented by –3x – 2y = 6.

To determine the relationship between line BC and line AD, first find the slope of both the lines using slope intercept form, that is:

$y=mx+c$  ----- (1)

Now, comparing both the equation of lines with equation (1).

Line BC becomes  --      $y = \dfrac{-3}{2}x+4$

Therefore, slope of line BC is $(-3\div2)$.

Line AD becomes  --    $y = \dfrac{-3}{2}x-3$

Therefore, slope of line AD is $(-3\div 2)$.

If the slope of two lines are same then they are parallel to each other. Therefore, line BC and line AD are parallel to each other.

Now, if we sum up both the equation of line:

$3x+2y-3x-2y=8+6$

0 = 14

This imply that both the lines AD and BC are parallel to each other.

For more information, refer the link given below:

https://brainly.com/question/12420847