Answer:
To find the equation of a line parallel to a given line and passing through a given point, we can use the fact that parallel lines have the same slope.
The given line has an equation of y = -3x + 2, where the slope is -3. Since we want to find a line parallel to this, the slope of the new line will also be -3.
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values into the equation.
Given point: (-2, -6)
Slope: -3
Substituting these values into the point-slope form, we get:
y - (-6) = -3(x - (-2))
Simplifying further:
y + 6 = -3(x + 2)
Expanding the brackets:
y + 6 = -3x - 6
Moving terms around to isolate y:
y = -3x - 6 - 6
Simplifying:
y = -3x - 12
Therefore, the equation of the line parallel to y = -3x + 2 and passing through (-2, -6) is y = -3x - 12.
Explanation: