Question

How to find the slope of each line on the figures below? Are the lines parallel?

Answer 1

`"see explanation"`

Explanation:

`• " Parallel lines have equal slopes"`

`"using the "color(blue)"definition of slope m"`

`•color(white)(x)m="difference in y"/"difference in x"=(Deltay)/(Deltax)`

`"use the usual convention in differences"`

`rarr(+)larr(-)uarr(+)darr(-)`

`"this ensures the sign of the slope is correct"`

`color(blue)"In general"`

`• " lines sloping upwards from left to right have a "`
`color(white)(xxx)"positive slope"`

`• " lines sloping downwards from left to right have a "`
`color(white)(xxx)"negative slope"`

`(A)`

`m_(AB)==2/4=1/2`

`m_(CD)=2/4=1/2`

`rArr"AB and CD are parallel"`

`(B)`

`m_(AB)=(-4)/2=-1/2`

`m_(CD)=(-3)/2=-3/2`

`rArr"AB and CD are not parallel"`

`(C)`

`m_(AB)=4/1=4`

`m_(CD)=4/1=4`

`rArr"AB and CD are parallel"`