Algebra 19 - Linear Equations y = mx

Professor Von Schmoke introduces real-valued functions and their representation on the Cartesian plane. The video explains linear functions, their equations, and how they are graphed. It discusses the role of coefficients in determining the slope of a line, including positive and negative slopes. The video also covers horizontal and vertical lines, emphasizing the relationship between coefficients and graph slopes.

What is the dependent variable typically assigned to when x is used as the input variable?

• a

• b

• y

• z

Why are linear functions considered important in mathematics?

• They are complex and difficult to understand.

• They can model many natural phenomena and appear linear on a small scale.

• They are only used in geometry.

• They do not have any practical applications.

What does the equation y = x imply about the coordinates of points on the line?

• x and y are always different.

• x is always greater than y.

• x and y have the same value.

• x is always less than y.

How can you verify if a point lies on the line described by an equation?

• By checking if the coordinates create a false statement.

• By replacing the variables in the equation with the coordinates and checking for a true statement.

• By ensuring the x-coordinate is always zero.

• By ensuring the y-coordinate is always zero.

What happens to the slope of a line when the x coefficient is negative?

• The line becomes vertical.

• The line slopes downwards.

• The line becomes horizontal.

• The line slopes upwards.

What does an x coefficient of zero indicate about the graph of the equation?

• The graph is a vertical line.

• The graph is a horizontal line.

• The graph is a diagonal line.

• The graph is a curved line.

Can an equation with a finite x coefficient describe a vertical line?

• Yes, any equation can describe a vertical line.

• No, it requires an infinitely large x coefficient.

• No, vertical lines cannot be described by equations.

• Yes, if the y coefficient is zero.