Question

Need an explanation, thx

Answer 1

Check out the attached photo

Answer 2

see explanation

Explanation:

calculate the slope m using the slope formula and equate to the given slope

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

(a)

(x₁, y₁ ) = (- 3, - 4 ) and (x₂, y₂ ) = (0, y )

`(y-(-4))/(0-(-3))` =
`(y+4)/(0+3)` =
`(y+4)/(3)` , then

`(y+4)/(3)` = 2 ( multiply both sides by 3 )

y + 4 = 6 ( subtract 4 from both sides )

y = 2

ordered pair is (0, 2 )

(b)

(x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (x, 5 )

`(5-2)/(x-(-2))` =
`(3)/(x+2)` , then

`(3)/(x+2)` =
`(3)/(7)` ( cross- multiply )

3(x + 2) = 21 ( divide both sides by 3 )

x + 2 = 7 ( subtract 2 from both sides )

x = 5

ordered pair is (5, 5 )

(c)

(x₁, y₁ ) = (x, 5 ) and (x₂, y₂ ) = (1, - 5 )

`(-5-5)/(1-x)` =
`(-10)/(1-x)` , then

`(-10)/(1-x)` =
`(-5)/(2)` ( cross- multiply )

- 5(1 - x) = - 20 ( divide both sides by - 5 )

1 - x = 4 ( subtract 1 from both sides )

- x = 3 ( multiply both sides by - 1 )

x = - 3

ordered pair is (- 3, 5 )

(e)

(x₁, y₁ ) = (- 6, y ) and (x₂, y₂ ) = (8, 2 )

`(2-y)/(8-(-6))` =
`(2-y)/(8+6)` =
`(2-y)/(14)` , then

`(2-y)/(14)` = -
`(1)/(7)` ( cross- multiply )

- 7(2 - y) = 14 ( divide both sides by - 7 )

2 - y = - 2 ( subtract 2 from both sides )

- y = - 4 ( multiply both sides by - 1 )

y = 4

ordered pair is (- 6, 4 )