Question

Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form? Y – 6 = y minus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x minus 2 right parenthesis.(x – 2) y – 6 = y minus 6 equals StartFraction 2 Over 5 EndFraction left-parenthesis x minus 2 right parenthesis.(x – 2) y + 6 = y plus 6 equals StartFraction 2 Over 5 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2) y + 6 = y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2)

Answer 1

Option D y + 6 = y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2)

Explanation:

Answer 2

Part 1)
`y+6=(2)/(5)(x+2)`

Part 2)
`y+6=(5)/(2)(x+2)`

Explanation:

The equation of the line in point slope form is

`y-y1=m(x-x1)`

we're going to analyze two cases

First case

`Point\ (-2,-6)`

`slope\ m=(2)/(5)`

substitute

`y+6=(2)/(5)(x+2)`

therefore

y plus 6 equals StartFraction 2 Over 5 EndFraction left-parenthesis x plus 2 right parenthesis

Second case

`Point\ (-2,-6)`

`slope\ m=(5)/(2)`

substitute

`y+6=(5)/(2)(x+2)`

therefore

y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis