Question

16. Calculate the slope of the line that passes through the two points (-4,2) and (1,3).

17. Calculate the slope of the line that passes through the two points (-1,-2) and (2,7).
18. Identify the slope and y intercept of the following equation. 4y=x+8
19. Identify the slope and y intercept of the following equation. 3x+9y=56
If you can please show your work

Answer 1

Question 16

(-4 , 2) (1 , 3)

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

Insert values into formula

`slope=(3-2)/(1-(-4))`

`slope=(1)/(5)`

Answer: slope = 1/5 or 0.2

Question 17

(-1 , -2) (2 , 7)

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

Insert values into formula

`slope=(7-(-2))/(2-(-1))`

`slope=(9)/(3)`

`slope=3`

Answer: slope = 3

Question 18

`4y=x+8`

Divide each term in the equation by 4 to get it into the form
`y=mx+c` where m=slope and c=y intercept

`4y/4=x/4+8/4`

`y=(1)/(4) x+2`

Now that the equation is in the form
`y=mx+c` the slope and y intercept can be identified.

slope = 1/4

y intercept = 2

Answer: slope = 1/4 and y intercept = 2

Question 19

`3x+9y=56`

We have to rearrange the equation into the form
`y=mx+c` where m=slope and c=y intercept

`9y=-3x+56`

Divide each term in the equation by 9 to get it into the form
`y=mx+c` where m=slope and c=y intercept

`9y/9=-3x/9+56/9`

`y=-(1)/(3)x+(56)/(9)`

Now that the equation is in the form
`y=mx+c` the slope and y intercept can be identified.

slope =
`-(1)/(3)`

y intercept = 56/9

Answer: slope =
`-(1)/(3)` and y intercept = 54/9