Understanding Linear Functions and Graphs

The video tutorial explains linear functions, focusing on graphs of the forms y = x and y = mx. It covers plotting points, constant rates of change, and the impact of different coefficients on the slope of the line. The tutorial also discusses how changing the coefficient affects the graph's linearity and slope direction, whether positive, negative, or zero. The lesson concludes with a summary of linear functions and their characteristics.

What is the first step in plotting a point on a graph?

• Begin at the end of the graph

• Move along the y-axis

• Start at the top of the graph

• Move along the x-axis

What is the relationship between x and y in the graph of y = x?

• y is always greater than x

• y is always less than x

• y is equal to x

• y is the square of x

What does a constant rate of change indicate about a graph?

• The graph is a parabola

• The graph is a curve

• The graph is a straight line

• The graph is a circle

In the function y = 1/2x, what is the role of 1/2?

• It is the y-intercept

• It is the slope

• It is the x-intercept

• It is the exponent

How does changing the coefficient of x to a negative value affect the graph?

• It becomes a curve

• It remains a straight line

• It becomes a circle

• It becomes a parabola

What happens to the graph when the coefficient of x is zero?

• The graph is a curve

• The graph is a vertical line

• The graph is a horizontal line

• The graph is a diagonal line

What is the slope of a line when the coefficient of x is positive?

• Zero slope

• Positive slope

• Undefined slope

• Negative slope

What does a greater absolute value of the coefficient of x indicate?

• A steeper slope

• A flatter slope

• A curved slope

• A horizontal slope

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

• Positive slope

• Undefined slope

• Negative slope

• Zero slope

What is the form of a linear function that passes through the origin?

• y = x + c

• y = x^2

• y = mx

• y = mx + b