Understanding Linear Functions and Their Properties

This video tutorial explains linear functions, focusing on their definition, characteristics, and analysis through graphs and tables. It covers the slope-intercept form, the impact of adding values to equations, and real-world applications like bank account balances. The tutorial emphasizes the constant rate of change in linear functions and concludes with a summary of key concepts.

What is a key characteristic of linear functions?

• They always pass through the origin.

• They have a constant rate of change.

• They form a curved line on a graph.

• They have a variable rate of change.

In the context of linear functions, what does a constant rate of change imply?

• The function is quadratic.

• The function is exponential.

• The function is logarithmic.

• The function is linear.

What happens to the graph of a linear equation when a constant is added to the x-term?

• The slope of the line changes.

• The line becomes curved.

• The line disappears.

• The line shifts vertically.

In the equation b = -7.5m + 50, what does the -7.5 represent?

• The constant term

• The x-intercept

• The y-intercept

• The slope

If the slope m is negative, what does it indicate about the line?

• The line slopes upward.

• The line slopes downward.

• The line is vertical.

• The line is horizontal.

How does subtracting a value from the x-term affect the linearity of a function?

• It makes the function non-linear.

• It changes the y-intercept.

• It does not affect the linearity.

• It changes the slope of the function.

What is the y-intercept in the equation y = mx + b?

• The point where the line crosses the x-axis

• The slope of the line

• The point where the line crosses the y-axis

• The steepness of the line

What does the slope-intercept form of a line allow you to determine?

• The x-intercept and y-intercept

• The area under the line

• The rate of change and y-intercept

• The curvature of the line

What is the effect of a positive y-intercept on the graph of a linear function?

• The graph shifts up.

• The graph shifts down.

• The graph becomes steeper.

• The graph becomes flatter.

What is the role of the constant b in the equation y = mx + b?

• It determines the curvature of the line.

• It determines the slope of the line.

• It determines the y-intercept of the line.

• It determines the x-intercept of the line.