Graphing and Analyzing Linear Functions

The video tutorial explains how to identify linear functions by plotting ordered pairs on a coordinate plane and analyzing their alignment. It covers determining the slope and correlation of points, whether positive or negative, and discusses how to identify linear patterns even when points are not equally spaced. The tutorial also demonstrates how to find outputs from given inputs on a graph and determine the slope direction. The video concludes with examples of both linear and non-linear functions.

What is the first step in plotting ordered pairs on a coordinate plane?

• Identify the slope of the line

• Determine the quadrant for each point

• Calculate the distance between points

• Find the midpoint of the line

How can you confirm that a set of points forms a linear function?

• The points form a circle

• The points are equally spaced

• The points align along a straight line

• The points are in different quadrants

What indicates a positive slope in a graph?

• The line moves downward from left to right

• The line is horizontal

• The line is vertical

• The line moves upward from left to right

What does a negative slope indicate about the direction of the line?

• The line moves upward from left to right

• The line is horizontal

• The line moves downward from left to right

• The line is vertical

In which quadrant would the point (4, -6) be located?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

What does it mean if x and y values are both decreasing?

• There is a positive correlation

• The points are not linear

• There is no correlation

• There is a negative correlation

Why might some students be confused by points that are not equally spaced?

• They assume equal spacing is necessary for linearity

• They think unequal spacing means non-linearity

• They expect all points to have the same y-value

• They believe all points should be in the same quadrant

What is the significance of points not lining up in a straight line?

• The function is linear

• The function is non-linear

• The points are equally spaced

• The points are in the same quadrant

What should you do if a point on a graph does not line up perfectly?

• Ignore the point

• Estimate the closest value

• Recalculate the slope

• Move the point to fit the line

How do you determine the y-value for a given x-value on a graph?

• Calculate the slope

• Find where the x-value intersects the line

• Find where the x-value intersects the y-axis

• Use the midpoint formula