Question

Find an equation of the line that contains the given pair of points. (-11, 9), (-9,-9)

Answer 1

Answer: y = -9x - 90

Explanation:

Our task is to write the equation of the line, given that it contains the following pair of points:

• (-11,9) and (-9,-9)

We will first find the line's slope.

Use the slope formula:

`m=\cfrac{y_2-y_1}{x_2-x_1}`

`m=\cfrac{-9-9}{-9-(-11)}`

`m=\cfrac{-18}{-9+11}`

`m=\cfrac{-18}{2}`

`m=-9`

The slope is 9; so far, the line's equation is:

`y-y_1=-9(x-x_1)`

Now, we also need the values of y_1 and x_1; we have them, y_1 is 9 and x_1 is -11, so we plug them in:

`y-9=-9(x-(-11)`

`y-9=-9(x+11)`

`y-9=-9x-99`

`y=-9x-99+9`

`y=-9x-90`

Therefore, our equation is y = -9x - 90.

Answer 2

Therefore, the equation of the line passing through the points (-11, 9) and (-9, -9) is y = -9x - 90.

Explanation:

To find the equation of the line passing through the points (-11, 9) and (-9, -9), we first find the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values of the points (-11, 9) and (-9, -9), we have:

m = (-9 - 9) / (-9 - (-11))

= -18 / 2

= -9

Now, we can use the point-slope form equation of a line, y - y1 = m(x - x1), where (x1, y1) is either of the given points. Let's use the first point (-11, 9):

y - 9 = -9(x - (-11))

y - 9 = -9(x + 11)

y - 9 = -9x - 99

y = -9x - 99 + 9

y = -9x - 90

Therefore, the equation of the line passing through the points (-11, 9) and (-9, -9) is y = -9x - 90.