Question

Help even tho it’s multiple choice make sure you are correct... I beg you lol

Answer 1

The equation of the line is:

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

Therefore, option a is the correct answer.

Explanation:

Given the points

• (-2, 2)

• (4, -1)

Finding the slope

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-2,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:-1\right)`

`m=(-1-2)/(4-\left(-2\right))`

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

As the point-slope form of the equation of the line is

`y-y_1=m\left(x-x_1\right)`

where m is the slope

substituting the values
`m=-(1)/(2)` and the point (-2, 2)

`y-y_1=m\left(x-x_1\right)`

`y-2=(-1)/(2)\left(x-\left(-2\right)\right)`

`y-2=(-1)/(2)\left(x+2\right)`

`y-2=-(1)/(2)\left(x+2\right)` ∵
`\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(b)=-(a)/(b)`

Add 2 to both sides

`y-2+2=-(1)/(2)\left(x+2\right)+2`

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

Hence, the equation of the line is:

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

Therefore, option a is the correct answer.