Linear Functions and Their Properties

The video tutorial explains how to write the equation of a linear function with a given slope and a point. It covers the slope-intercept form, substitution to find the intercept, and verification of the equation by graphing. The tutorial emphasizes understanding the slope and intercept and demonstrates solving for the intercept using substitution.

What is the first step in finding the equation of a linear function given a slope and a point?

• Calculate the slope

• Find the slope-intercept form

• Use the point-slope form

• Identify the y-intercept

In the slope-intercept form y = mx + b, what does 'm' represent?

• The y-intercept

• The y-coordinate

• The slope of the line

• The x-coordinate

Given the slope -38 and a point (4, 2), what is the initial form of the equation?

• y = 38x - b

• y = -38x - b

• y = 38x + b

• y = -38x + b

What is the purpose of substituting the point (4, 2) into the equation y = -38x + b?

• To verify the equation

• To find the slope

• To determine the x-coordinate

• To solve for the y-intercept

After substituting the point into the equation, what operation is performed to isolate b?

• Subtraction

• Division

• Addition

• Multiplication

What is the value of the vertical intercept 'b' after simplification?

• 5

• 2

• 7

• 3

What is the final equation of the linear function after finding b?

• y = -38x + 7

• y = -38x - 7

• y = 38x + 7

• y = 38x - 7

How can you verify that the derived equation is correct?

• By checking the slope

• By plotting the point and graphing the line

• By recalculating the slope

• By finding another point

What should you do if the line does not pass through the given point after graphing?

• Change the slope

• Recalculate the y-intercept

• Check the calculations

• Use a different point

What is the significance of the point (4, 2) in the context of the equation?

• It is the origin

• It is the slope

• It is a point on the line

• It is the y-intercept