Transformations of Linear Equations

This video tutorial explains how transformations affect linear equations, covering translations, reflections, and scaling. It details how these transformations shift, mirror, or change the slope of linear functions. The tutorial also explains how to identify the value of k in transformations and provides examples of vertical and horizontal translations, reflections across axes, and scaling transformations.

What are the three main categories of transformations discussed in the lesson?

• Reflections, Rotations, Scaling

• Translations, Reflections, Scaling

• Translations, Rotations, Reflections

• Translations, Rotations, Scaling

How does a vertical translation affect the graph of a linear equation?

• It changes both the slope and the y-intercept.

• It changes the y-intercept but not the slope.

• It does not change the graph at all.

• It changes the slope but not the y-intercept.

In a horizontal translation, what remains unchanged?

• The x-values

• The y-intercept

• The y-values

• The slope

What happens to the slope and y-intercept when a reflection occurs across the x-axis?

• Only the y-intercept changes.

• They become the opposites of each other.

• Only the slope changes.

• They remain the same.

When reflecting across the y-axis, what happens to the x-coordinates?

• They are halved.

• They become the opposite value.

• They remain the same.

• They double in value.

What is the effect of a vertical stretch on a linear equation?

• The y-intercept moves closer to the x-axis.

• The y-intercept moves farther from the x-axis.

• The x-intercept changes.

• The slope becomes zero.

How does a horizontal compression affect the x-intercept?

• It moves closer to the y-axis.

• It becomes zero.

• It moves farther from the y-axis.

• It remains unchanged.

In a vertical scaling transformation, what is the role of the constant k?

• It divides the slope.

• It is added to the x-values.

• It is multiplied by the entire function.

• It is subtracted from the y-values.

What is the general rule for identifying k in horizontal scaling?

• g(x) = f(k * x)

• g(x) = k * f(x)

• g(x) = f(x - k)

• g(x) = f(x) + k

What is the primary effect of scaling transformations on a linear equation?

• They mirror the graph across an axis.

• They change the slope, making the graph flatter or steeper.

• They shift the graph up or down.

• They rotate the graph around the origin.