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

Answer:

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

.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 $x_{0} \ne x_{1}$,) 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:

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

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

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