Question

What is the equation of the line that passes through (-2, 2) and (1, -4)? y = 2x - 2,

y = -2x - 4,
y = -2x - 2,
y = 2x + 4,

Answer 1

The point-slope form of line:

`y-y_1=m(x-x_1)`

The fomula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

Substitute the coordinates of the points:

`m=(-4-2)/(1-(-2))=(-6)/(1+2)=(-6)/(3)=-2`

`y-(-4)=-2(x-1)` use distributive property

`y+4=-2x+2` subtract 4 from both sides

`\boxed{y=-2x-2}`

Answer 2

y = -2x-2

Explanation:

The line passes through the points (-2, 2) and (1, -4).

The slope of the line is given by

`m=(y_2-y_1)/(x_2-x_1)\\\\m=(-4-2)/(1+2)\\\\m=(-6)/(3)\\\\m=-2`

The slope intercept form of a line is given by

y = mx +b, where m is the slope and b is the y-intercept.

We have, m = -2. Hence, the equation is

y = -2x + b

Now, use the point (-2,2) to find b

2 = -2(-2) + b

2 = 4 +b

b = -2

Hence, the equation of the line is y = -2x-2

Third option is correct.