Exploring Linear Relations: The Equation y = mx + b

This video tutorial covers the basics of linear equations, focusing on the equation of a line, y = mx + b. It explains the roles of dependent and independent variables, the significance of the slope (m), and the y-intercept (b). The tutorial also distinguishes between direct and partial variations and demonstrates how to find the equation of a line using a plot. The video aims to provide a thorough understanding of linear relations and their components.

What does the variable 'Y' represent in a linear equation?

• Slope

• Independent variable

• Constant

• Dependent variable

In the context of linear equations, what is the role of the variable 'X'?

• Dependent variable

• Constant

• Independent variable

• Slope

What is another name for the constant 'M' in the equation of a line?

• Independent variable

• Dependent variable

• Rate of change

• Y-intercept

Which term is used to describe the steepness of a line in a linear equation?

• Dependent variable

• Slope

• Constant

• Y-intercept

How is the slope (M) of a line calculated?

• Difference of X and Y

• Run over rise

• Sum of X and Y

• Rise over run

What does the y-intercept (B) represent in a linear equation?

• The point where the line crosses the Y-axis

• The slope of the line

• The point where the line crosses the X-axis

• The dependent variable

What is another name for the y-intercept (B)?

• Slope

• Initial value

• Dependent variable

• Independent variable

What is a direct variation in the context of linear equations?

• A line with a y-intercept of zero

• A line that crosses the origin

• A line that crosses the Y-axis

• A line with a slope of zero

What is a partial variation in linear equations?

• A line with a y-intercept not equal to zero

• A line that crosses the origin

• A line that does not cross the Y-axis

• A line with a slope of zero

To derive the equation of a line from a graph, which two values are essential?

• Independent variable and constant

• X and Y

• Slope and dependent variable

• Slope and y-intercept