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

Answer:

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+cy=mx+c  ----- (1)

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

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

Therefore, slope of line BC is (-3\div2)(−3÷2) .

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

Therefore, slope of line AD is (-3\div 2)(−3÷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+63x+2y−3x−2y=8+6

0 = 14

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

Step-by-step explanation:

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+cy=mx+c  ----- (1)

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

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

Therefore, slope of line BC is (-3\div2)(−3÷2) .

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

Therefore, slope of line AD is (-3\div 2)(−3÷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+63x+2y−3x−2y=8+6

0 = 14

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