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 the sum if the equations demonstrates the relationship

Answer 1

The answer is below

Explanation:

The equation of a straight line is given by:

y = mx + b

where m is the slope of the line and b is the y intercept (value of y when x = 0).

Given the equation of two lines as
`y=m_1x+b_1\ and\ y=m_2x+b_2`, the two lines are parallel to each other if
`m_1=m_2`. Also the lines are perpendicular if

`m_1m_2=-1`

Given line BC:

3x + 2y = 8

2y = -3x + 8

y = -3x/2 + 4

Hence the slope of the line BC = -3/2

For line AD:

-3x - 2y = 6

-2y =3x + 6

y = -3x/2 - 3

Hence the slope of line AD is -3/2

Since both line BC and AD have equal slope (-3/2), hence both lines are parallel to each other