Question

Line 1: 4x + 2y = 12

Line 2: 3x - 6y =18

State the slope of each line, then determine if the lines are parallel, perpendicular, or neither.

slope of line 1 =

slope of line 2 =

Are the lines parallel, perpendicular, or neither?

Answer 1

Slope of line one is -2 while the slope of line 2 is 1/2 (a half). And the lines are perpendicular I believe

Answer 2

lines are perpendicular

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

line 1

4x + 2y = 12 ( subtract 4x from both sides )

2y = - 4x + 12 ( divide through by 2 )

y = - 2x + 6 ← in slope- intercept form

slope of line 1 = - 2

line 2

3x - 6y = 18 ( subtract 3x from both sides )

- 6y = - 3x + 18 ( divide through by - 6 )

y =
`(1)/(2)` x - 3 ← in slope- intercept form

slope of line 2 =
`(1)/(2)`

• Parallel lines have equal slopes

Clearly the lines are not parallel

• the product of the slopes of perpendicular lines = - 1

- 2 ×
`(1)/(2)` = - 1

then Line 1 and Line 2 are perpendicular to each other