ANSWER
[tex]y - 4 = - \frac{1}{2} (x + 6)[/tex]
EXPLANATION
The given points are
[tex](-6,4) \: and \: (4,2)[/tex]
First, determine the slope using the formula,
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Let
[tex](x_1,y_1)=(-6,4).[/tex]
and
[tex](x_2,y_2)=(4,2)[/tex]
Then, the slope becomes,
[tex]m = \frac{2 - 4}{4 - - 6} [/tex]
[tex]m = \frac{2 - 4}{4 + 6} [/tex]
[tex]m = \frac{ - 2}{10} = - \frac{1}{5} [/tex]
The equation in point slope-form is given by the formula,
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the values to get,
[tex]y - 4 = - \frac{1}{2} (x - - 6)[/tex]
Therefore the point-slope form is
[tex]y - 4 = - \frac{1}{2} (x + 6)[/tex]
