Question

Find the slope of the lines. Are the 2 lines parallel or perpendicular? Explain how you can use the slope of two lines to tell if they are parallel. Then explain how you can use the slope of two lines to tell if they are perpendicular. 20 points!

Answer 1

slope =
`(3)/(7)` and -
`(7)/(3)`, perpendicular

Explanation:

the equation of a line in slope-intercept form is

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

y =
`(3)/(7)` x + 11 is in this form with m =
`(3)/(7)`

Rearrange 7x + 3y = 13 into this form

subtract 7x from both sides

3y = - 7x + 13 ( divide all terms by 3 )

y = -
`(7)/(3)` x +
`(13)/(3)` ← in slope- intercept form

with m = -
`(7)/(3)`

• Parallel lines have equal slopes

• The product of perpendicular slopes = - 1

The lines are not parallel since slopes are not equal

`(3)/(7)` × -
`(7)/(3)` = - 1

Hence lines are perpendicular