Question

Write an equation for the line in point slope form through the points (2, −6) and (−1, −8).

Answer 1

To write the equation for the line in point-slope form through the points (2, −6) and (−1, −8), we need to use the formula: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope. Using the points (2, -6) and (-1, -8), we can calculate the slope (m) as 2/3. Plugging this into the point-slope form equation, we obtain y = (2/3)x - 22/3.

Step-by-step explanation:

To write the equation for the line in point-slope form, we need to use the formula: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope.

Using the points (2, -6) and (-1, -8):

Slope (m) = (y2 - y1) / (x2 - x1) = (-8 - (-6)) / (-1 - 2) = -2 / -3 = 2/3

Now, we can use the point-slope form with one of the points:

y - (-6) = (2/3)(x - 2)

Expanding and simplifying the equation, we get:

y + 6 = (2/3)x - 4/3

y = (2/3)x - 4/3 - 6

y = (2/3)x - 22/3

Therefore, the equation for the line in point-slope form through the points (2, -6) and (-1, -8) is y = (2/3)x - 22/3.

Answer 2

Let point A be
`(2, -6)` and point B
`(-1, -8)`

`m = (y_2 - y_1)/(x_2 - x_1) = (-8 - (-6))/(-1 - 2) = (-8 + 6)/(-1 -2) = (-2)/(-3) = (2)/(3)`

Use the point-slope formula and whichever point you want as , in this case I'll use

`y - y_1 = m(x - x_1)\\y - (-6) = (2)/(3)(x - 2)\\y + 6 = (2)/(3)x - (4)/(3)\\y = (2)/(3)x - (4)/(3) - 6\\y = (2)/(3)x - (14)/(3)`