To find the equation of a line in point-slope form, we use the formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\((x_1, y_1)\)[/tex] are the coordinates of a point on the line.
Given:
- The slope, [tex]\( m \)[/tex], is [tex]\(-2\)[/tex].
- The point [tex]\((x_1, y_1)\)[/tex] through which the line passes is [tex]\((4, -6)\)[/tex].
Now, substitute the given values into the point-slope form formula:
[tex]\[ y - (-6) = -2(x - 4) \][/tex]
Simplify the equation:
[tex]\[ y + 6 = -2(x - 4) \][/tex]
Thus, the point-slope form of the equation for the line with a slope of [tex]\(-2\)[/tex] that passes through the point [tex]\((4, -6)\)[/tex] is:
[tex]\[ y + 6 = -2(x - 4) \][/tex]
Therefore, the correct option is:
[tex]\[ y + 6 = -2(x - 4) \][/tex]
