Understanding Linear Functions and Equations

The video tutorial explains how to write the equation of a linear function from a given table of values. It covers finding the slope using two ordered pairs, determining the vertical intercept through substitution, and expressing the equation in both standard and function notation. The tutorial concludes with a verification step by graphing the function and checking the alignment of points.

What is the first step in finding the equation of a linear function from a table of values?

• Identify the y-intercept

• Find the slope using two ordered pairs

• Graph the points on a coordinate plane

• Use function notation

How do you calculate the slope (m) of a linear function?

• Multiply the x and y values

• Subtract the x values from the y values

• Divide the change in x by the change in y

• Divide the change in y by the change in x

What is the slope of the linear function derived from the table?

• 3.2

• 2.9

• 0.6

• 0.3

Which ordered pair is used to find the vertical intercept (b) after finding the slope?

• The pair with the largest x value

• Any ordered pair from the table

• The pair with the smallest y value

• The pair where x equals zero

What is the equation of the linear function derived from the table?

• y = 0.3x + 3.2

• y = 0.3x + 2.9

• y = 0.6x + 2.9

• y = 0.6x + 3.2

What is the vertical intercept (b) of the linear function?

• 0.3

• 0.6

• 2.9

• 3.2

What alternative notation can be used for the linear function equation?

• J(x)

• F(x)

• G(x)

• H(x)

What is the purpose of using function notation in linear equations?

• To change the slope

• To simplify the equation

• To express the equation as a function of x

• To make the equation more complex

How can you verify the correctness of the linear equation?

• By graphing the ordered pairs and the equation

• By using a different pair of points

• By checking the table values

• By recalculating the slope

What should be true if the linear equation is correct when graphed?

• The line should be vertical

• The ordered pairs should lie on the line

• The line should be horizontal

• The line should pass through the origin