Linear Tables

What is a linear table?

• A table of values that represents a linear function, where the relationship between the input (x) and output (y) is constant, resulting in a straight line when graphed.

• A table that displays random values without any specific relationship.

• A table that shows the relationship between two variables in a non-linear fashion.

• A table that only includes integer values without any decimal points.

How can you determine if a function is linear from a table?

• A function is linear if the differences between consecutive y-values divided by the differences between consecutive x-values (the slope) are constant.

• A function is linear if all y-values are positive.

• A function is linear if the x-values are in ascending order.

• A function is linear if the graph forms a curve.

What does it mean if a function has a slope of zero?

• A slope of zero indicates a vertical line, meaning there is no change in x as y changes.

• A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

• A slope of zero indicates an increasing line, meaning y increases as x increases.

• A slope of zero indicates a decreasing line, meaning y decreases as x increases.

What is the significance of the slope in a real-world context?

• It represents the distance between two points on a graph.

• It can indicate the rate of change, such as speed or cost per item.

• It shows the maximum value of a function.

• It determines the area under a curve.

What does the term 'nonlinear' mean?

• A relationship between variables that forms a straight line when graphed.

• A relationship between variables that does not form a straight line when graphed, indicating a varying rate of change.

• A relationship that is constant and does not change over time.

• A relationship that can only be represented by a quadratic equation.

How can you identify the slope from a table of values?

• By calculating the change in y divided by the change in x between two points in the table.

• By finding the average of all y-values in the table.

• By determining the maximum y-value and the minimum x-value.

• By plotting the points on a graph and drawing a line through them.

How do you find the y-intercept from a table?

• By identifying the value of y when x is 0 in the table.

• By averaging all the y values in the table.

• By finding the maximum value of y in the table.

• By calculating the slope of the line represented in the table.

What is the slope of a line?

• A measure of its length

• The change in y divided by the change in x (rise/run)

• The angle it makes with the x-axis

• The distance between two points on the line

What is the equation of a line in slope-intercept form?

• y = mx + b

• y = mx - b

• y = b - mx

• y = m + b

What is the relationship between the slope and the steepness of a line?

• The greater the absolute value of the slope, the steeper the line.

• A slope of 0 is the steepest line.

• A slope of -1 is steeper than a slope of 1.

• The slope does not affect the steepness of the line.