Question

Find the slope of the line through each pair of points. Pls help and explain if you cann!!

Answer 1

1) The slope for the given points (6,7) and (-10,4) is
`m=(3)/(16)`

2) The slope for the given points (17,4) and (13,20) is
`m=-4`

3) The slope for the given points (12,19) and (14,18) is
`m=-(1)/(2)`

4) The slope for the given points (-11,0) and (18,13) is
`m=(13)/(29)`

5) The slope for the given points (3,6) and (-8,20) is
`m=-(14)/(11)`

6) The slope for the given points (-16,-20) and (12,5) is
`m=(25)/(28)`

7) The slope for the given points (13,20) and (14,-14) is
`m=-34`

8) The slope for the given points (18,15) and (3,0) is
`m=1`

Explanation:

To find the slope of the line through each pair of points:

1) Given points are (6,7) and (-10,4)

The slope formula is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the given points (6,7) and (-10,4) respectively

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(4-7)/(-10-6)`

`m=(-3)/(-16)`

`m=(3)/(16)`

Therefore the slope for the given points (6,7) and (-10,4) is
`m=(3)/(16)`

2) Given points are (17,4) and (13,20)

The slope formula is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the given points (17,4) and (13,20) respectively

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(20-4)/(13-17)`

`m=(16)/(-4)`

`m=-4`

Therefore the slope for the given points (17,4) and (13,20) is
`m=-4`

3) Given points are (12,19) and (14,18)

The slope formula is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the given points (12,19) and (14,18) respectively

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(18-19)/(14-12)`

`m=(-1)/(2)`

Therefore the slope for the given points (12,19) and (14,18) is
`m=-(1)/(2)`

4) Given points are (-11,0) and (18,13)

The slope formula is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the given points (-11,0) and (18,13) respectively

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(13-0)/(18-(-11))`

`m=(13)/(29)`

Therefore the slope for the given points (-11,0) and (18,13) is
`m=(13)/(29)`

5) Given points are (3,6) and (-8,20)

The slope formula is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the given points (3,6) and (-8,20) respectively

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(20-6)/(-8-3)`

`m=(14)/(-11)`

`m=-(14)/(11)`

Therefore the slope for the given points (3,6) and (-8,20) is
`m=-(14)/(11)`

6) Given points are (-16,-20) and (12,5)

The slope formula is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the given points (-16,-20) and (12,5) respectively

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(5-(-20))/(12-(-16))`

`m=(5+20)/(12+16)`

`m=(25)/(28)`

Therefore the slope for the given points (-16,-20) and (12,5) is
`m=frac{25}{28}`

7) Given points are (13,20) and (14,-14)

The slope formula is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the given points (13,20) and (14,-14) respectively

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(-14-20))/(14-13)`

`m=(-34)/(1)`

`m=-34`

Therefore the slope for the given points (13,20) and (14,-14) is
`m=-34`

8) Given points are (18,15) and (3,0)

The slope formula is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the given points (18,15) and (3,0) respectively

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(0-15)/(3-18)`

`m=(-15)/(-15)`

`m=1`

Therefore the slope for the given points (18,15) and (3,0) is
`m=1`