Understanding Linear Functions and Graphs

The video tutorial explains how to identify linear functions by plotting ordered pairs on a coordinate plane. It covers how to determine if a function is linear by checking if points align in a straight line. The video also discusses positive and negative slopes, and how to interpret them. It further explores how to find outputs from given inputs using graphs, and identifies non-linear functions where points do not align. The tutorial emphasizes understanding the correlation between x and y values and how to visually interpret these relationships on a graph.

What is the main characteristic of a linear function when plotted on a graph?

• The points form a circle.

• The points align in a straight line.

• The points form a zigzag pattern.

• The points are scattered randomly.

How can you identify a positive slope on a graph?

• The line moves downward from left to right.

• The line is vertical.

• The line is horizontal.

• The line moves upward from left to right.

What indicates a negative slope in a set of points?

• Both x and y values increase.

• x values increase while y values decrease.

• Both x and y values decrease.

• x values decrease while y values increase.

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

• Quadrant 4

• Quadrant 2

• Quadrant 1

• Quadrant 3

What is a key feature of a positive correlation in a graph?

• Points move in the same direction.

• Points form a zigzag pattern.

• Points are scattered randomly.

• Points move in opposite directions.

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

• They believe points should be in one quadrant.

• They expect points to form a circle.

• They think unequal spacing means non-linearity.

• They assume all linear functions have equally spaced points.

What is the result when points do not align in a straight line?

• The function has a positive slope.

• The function is non-linear.

• The function is linear.

• The function has a negative slope.

When estimating values on a graph, what should you do if points don't align perfectly?

• Ignore the points.

• Panic and start over.

• Use only exact values.

• Estimate the closest value.

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

• The line moves downward from left to right.

• The line is vertical.

• The line is horizontal.

• The line moves upward from left to right.

How do you determine the output for a given input using a graph?

• By guessing the value.

• By checking where the input aligns on the y-axis.

• By looking at the x-axis only.

• By drawing a new line.