Understanding Linear Functions through Graph Analysis

This video tutorial explains linear functions, focusing on the forms y = x and y = mx. It covers plotting points on a graph, understanding the concept of slope, and analyzing how different coefficients affect linearity. The video demonstrates that linear functions have a constant rate of change, regardless of the coefficient's value, whether positive, negative, or zero. It also highlights the importance of the slope, represented by the coefficient m, in determining the line's steepness and direction.

What is the key characteristic of a linear function?

• It forms a zigzag pattern.

• It forms a curved line.

• It has a constant rate of change.

• It has a variable rate of change.

How does changing the coefficient of x affect the function y = mx?

• It changes the y-intercept.

• It makes the line disappear.

• It changes the slope of the line.

• It makes the function nonlinear.

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

• The slope becomes undefined.

• The slope becomes negative.

• The slope becomes positive.

• The slope becomes zero.

What is the slope of the line when the coefficient of x is zero?

• Positive

• Undefined

• Zero

• Negative

How does the absolute value of the coefficient of x affect the line?

• It changes the color of the line.

• It makes the line disappear.

• It affects the steepness of the slope.

• It changes the y-intercept.

What distinguishes a nonlinear function from a linear function?

• A nonlinear function passes through the origin.

• A nonlinear function forms a straight line.

• A nonlinear function has a variable rate of change.

• A nonlinear function has a constant rate of change.

In a nonlinear function, how does the rate of change behave?

• It remains constant.

• It varies depending on the points chosen.

• It is always positive.

• It is always zero.