Question

Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither 3x+5y=10 and 5x-3y=-6

Answer 1

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 )

3x + 5y = 10 ( subtract 3x from both sides )

5y = - 3x + 10 ( divide through by 5 )

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

with slope m = -
`(3)/(5)`

---------------------------

5x - 3y = - 6 ( subtract 5x from both sides )

- 3y = - 5x - 6 ( divide through by - 3 )

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

with slope m =
`(5)/(3)`

---------------------------

• Parallel lines have equal slopes

clearly the lines are not parallel

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

-
`(3)/(5)` ×
`(5)/(3)` = - 1

thus the 2 lines are perpendicular to each other