Final answer:
To find the equation of the line parallel to line k and passing through the point (4,-4), we differentiate the equation of line k to find its slope. We then use the slope to determine the equation of the parallel line through the given point.
Step-by-step explanation:
Given the equation for line k as y³ = – 3(x–7), we need to find the equation of a line that is parallel to line k and passes through the point (4,– 4).
To find the equation of a line parallel to line k, we need to find the slope of line k. The slope of line k can be determined by taking the derivative of the given equation.
To find the slope of line k at any point (x, y), we can differentiate the equation with respect to x: dy/dx = -3
Since the line parallel to line k will have the same slope, the equation of the line passing through the point (4,-4) can be written as y - (-4) = -3(x - 4)
Simplifying the equation, we get y + 4 = -3x + 12.
The final equation of the line that is parallel to line k and passes through the point (4,– 4) is y = -3x + 8.