Kg passes through the point (2, 14) and intersects hg at the point (12, 4). if the point h(18, 10) lies on hg, write the equation, in point slope form, of each line.

The equation for KG would be y-14=-1(x-2) and the equation for HG would be y-4=1(x-12).

We first find the slope of KG.  The formula for slope is
m=(y₂-y₁)/(x₂-x₁)

Using the points we have for KG, we have
m=(4-14)/(12-2) = -10/10 = -1

The equation for point-slope form is
y-y₁=m(x-x₁)

Using the slope of KG and the first point listed for that line, we have
y-14=-1(x-2)

Now we find the slope of HG:
m=(10-4)/(18-12) = 6/6 = 1

Using the point of intersection for KG and HG, we have
y-4=1(x-12)