Question

Write the equation of the line that passes through the points (0,8) and (6,-2). Put

your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.

Answer 1

`y - (-2) = (-5/3)\, (x - 6)`.

.Step-by-step explanation:

The
`x`-coordinates of the two given points are different. Therefore, the line that goes through these points would not be vertical. Likewise, this line would not be horizontal since the
`y`-coordinates of the given points are different.

If a line in a plane is of slope
`m` and goes through point
`(x_(0),\, y_(0))`, the point-slope equation of this line would be
`y - y_(0) = m\, (x - x_(0))`.

If a line in a plane goes through the points
`(x_(0),\, y_(0))` and
`(x_(1),\, y_(1))` (where
`x_(0) \\e x_(1)`,) the slope of this line would be
`m = (y_(1) - y_(0)) / (x_(1) - x_(0))`.

Since the line in this question goes through points
`(6,\, -2)` and
`(0,\, 8)`, the slope of this line would be:

`\begin{aligned} m &= (8 - (-2))/(0 - 6) \\ &= (10)/((-6)) \\ &= -(5)/(3)\end{aligned}`.

Let
`(6,\, -2)` be the point
`(x_(0),\, y_(0))`. The point-slope equation of this line would be:

`y - (-2) = (-5 / 3)\, (x - 6)`.