White the equation of the line that passes through the points o(0,8) and 6,-2. Put your answer in fully simplified point-slope form unless it is a vertical or horizontal line

Answer 1

To find the equation of the line passing through the points (0,8) and (6,-2), we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

where (x₁, y₁) represents one of the points on the line, and "m" represents the slope.

First, let's find the slope of the line:
m = (y₂ - y₁) / (x₂ - x₁)

Using the coordinates of the two points, we find:
m = (-2 - 8) / (6 - 0)
m = -10 / 6
m = -5/3

We have the slope; now let's choose a point (x₁, y₁) from either of the given points. Let's use (0,8) as our point.

Plugging in the values into the point-slope form, we get:
y - 8 = (-5/3)(x - 0)

Simplifying further, we have:
y - 8 = (-5/3)x

So, the equation of the line passing through the points (0,8) and (6,-2) in the point-slope form is:
y - 8 = (-5/3)x