Exploring Linear Transformations

The video tutorial covers linear transformations, focusing on reflection, steepness, and vertical shifts in linear functions. It explains the components of linear equations, such as the slope and y-intercept, and how they affect the graph. The tutorial includes examples and practice exercises to help students understand and apply these concepts.

What is the basic form of a linear equation?

• y = e^x

• y = a/x

• y = ax^2 + bx + c

• y = mx + b

What does a negative sign directly after the equal sign indicate?

• The graph shifts up

• The graph becomes steeper

• The graph shifts down

• The graph reflects

If the slope (a) is greater than 1, what does it indicate about the graph?

• The graph reflects

• The graph is more steep

• The graph is less steep

• The graph shifts down

What does the y-intercept (b) represent in the equation y = mx + b?

• The slope of the graph

• The point where the graph crosses the y-axis

• The point where the graph crosses the x-axis

• The steepness of the graph

What happens to the graph when you add a positive constant to the y-intercept?

• The graph shifts down

• The graph reflects

• The graph shifts up

• The graph becomes less steep

How do you determine if a slope is less steep?

• If the slope is greater than 1

• If the slope is negative

• If the slope is equal to 1

• If the slope is less than 1

What does a slope of 1/4 indicate about the graph?

• The graph is more steep

• The graph is less steep

• The graph reflects

• The graph shifts up

What does a negative slope do to the graph?

• Shifts the graph up

• Shifts the graph down

• Makes the graph steeper

• Reflects the graph

In the equation f(x) = -2x + 10, what does the -2 represent?

• The graph shifts up

• The graph reflects

• The graph shifts down

• The graph becomes less steep

In the equation f(x) = 2/3x + 1, what does the 2/3 indicate?

• The graph is less steep

• The graph is more steep

• The graph reflects

• The graph shifts down