Questions: Find the equation of the line that has the given properties. Contains (-6,-3); parallel to the line y=-4x-2 The equation of the parallel line is (Type your answer in slope-intercept form.)

To find the equation of a line that passes through a given point and is parallel to another line, we need to use the slope of the given line. Since parallel lines have the same slope, we can use the slope from the given line and the point-slope form of a line equation to find the desired line's equation.

1. Identify the slope of the given line.
2. Use the point-slope form of the line equation with the given point and the identified slope.
3. Convert the equation to slope-intercept form.

La ecuación de la línea dada es \( y = -4x - 2 \). La pendiente \( m \) de esta línea es \( -4 \).

Dado que la línea que buscamos es paralela a la línea dada, tendrá la misma pendiente. Usamos la forma punto-pendiente de la ecuación de la línea: \[ y - y_1 = m(x - x_1) \] donde \( (x_1, y_1) = (-6, -3) \) y \( m = -4 \).

Sustituyendo los valores en la ecuación: \[ y - (-3) = -4(x - (-6)) \] Simplificando: \[ y + 3 = -4(x + 6) \] \[ y + 3 = -4x - 24 \] \[ y = -4x - 27 \]

La ecuación de la línea paralela es \\(\boxed{y = -4x - 27}\\).