What would the equation look like in a rotation of the linear parent function?
To understand the equation for a rotation of the linear parent function, let's start by considering the general equation of a linear function:
y = mx + b
In this equation, m represents the slope of the line, and b represents the y-intercept. The slope determines the steepness of the line, while the y-intercept represents the point where the line intersects the y-axis.
Now, if we want to rotate the linear parent function, we can do so by applying a transformation called a rotation. To rotate a function, we need to determine the angle of rotation and the center or point of rotation.
Let's say we want to rotate the linear function by an angle of θ degrees counterclockwise around a point (h, k). The new rotated function would have the equation:
y' = m'(x' - h) + k
To find the values of m' and (x', y'), we need to use rotation formulas:
x' = (x - h) * cos(θ) - (y - k) * sin(θ)
y' = (x - h) * sin(θ) + (y - k) * cos(θ)
Using these formulas, we can substitute x' and y' back into the equation of the linear parent function:
y' = m'(x' - h) + k
= m'((x - h) * cos(θ) - (y - k) * sin(θ)) + k
Simplifying this equation will give you the equation for a rotation of the linear parent function.
It's important to note that the rotated linear function will not always have a simple form like the original parent function. The equation will depend on the angle of rotation and the point of rotation.