Understanding Linear Functions and Graphs

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, distinguishing between positive and negative slopes, and recognizing non-linear functions. The tutorial also demonstrates how to find outputs from given inputs on a graph, emphasizing the importance of understanding point patterns and their spacing.

What is a key 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 moves upward from left to right.

• The line is horizontal.

What indicates a negative correlation between x and y values?

• Both x and y values increase.

• Both x and y values decrease.

• x values decrease while y values increase.

• x values increase while y values decrease.

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

• Quadrant 4

• Quadrant 2

• Quadrant 3

• Quadrant 1

What does it mean if points on a graph are not equally spaced but still form a line?

• The points are incorrect.

• The graph is incomplete.

• The function is non-linear.

• The function is linear.

Which of the following points is in Quadrant 3?

• (3, 5)

• (1, 1)

• (-2, -5)

• (4, 2)

What should you do if plotted points do not align in a straight line?

• Check for a positive slope.

• Check for a negative slope.

• Conclude it is not a linear function.

• Replot the points.

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

• By guessing the output.

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

• By drawing a new line.

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

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

• Ignore the point.

• Estimate the closest value.

• Recalculate the point.

• Move the point to the nearest line.

What type of slope is indicated if a line goes downward from left to right?

• Zero slope

• Positive slope

• Negative slope

• Undefined slope