Interpreting Linear Graphs

What does the term 'linear' mean in the context of graphs?

• Linear refers to a relationship that can be represented by a straight line on a graph.

• Linear refers to a relationship that can be represented by a curved line on a graph.

• Linear refers to a relationship that has no correlation on a graph.

• Linear refers to a relationship that can only be represented in three dimensions.

What does a negative slope indicate about a linear relationship?

• A negative slope indicates that as x increases, y decreases.

• A negative slope indicates that as x increases, y increases.

• A negative slope indicates that there is no relationship between x and y.

• A negative slope indicates that y is always zero.

What does the y-intercept represent in a linear graph?

• The value of y when x is 0, indicating the starting point of the relationship represented by the graph.

• The slope of the line, representing the rate of change of y with respect to x.

• The point where the line crosses the x-axis, indicating the value of x when y is 0.

• The maximum value of y in the graph, representing the highest point of the relationship.

How do you interpret the slope in a real-world context?

• The slope represents a fixed value that does not change over time.

• The slope can represent a rate of change, such as speed, cost per item, or growth rate.

• The slope indicates the total amount of change without regard to direction.

• The slope is only relevant in theoretical mathematics and has no real-world application.

What is the significance of the x-intercept in a linear graph?

• It represents the value of y when x is 0.

• It indicates where the graph crosses the y-axis.

• It is the value of x when y is 0, indicating where the graph crosses the x-axis.

• It shows the slope of the line.

How can you determine the slope from two points on a graph?

• The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of the two points.

• The slope is determined by finding the average of the y-coordinates of the two points.

• The slope can be calculated by adding the x-coordinates of the two points together.

• The slope is the distance between the two points divided by the time taken to travel between them.

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

• y = mx + b, where m is the slope and b is the y-intercept.

• y = b + mx, where b is the slope and m is the y-intercept.

• y = mx^2 + b, where m is the slope and b is the y-intercept.

• y = mx - b, where m is the slope and b is the y-intercept.

What does it mean if a line is horizontal on a graph?

• A horizontal line indicates that the value of y remains constant regardless of the value of x.

• A horizontal line indicates that the value of x remains constant regardless of the value of y.

• A horizontal line indicates that both x and y values are increasing.

• A horizontal line indicates that the graph is not changing over time.

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

• A steeper line has a larger absolute value of slope, indicating a greater rate of change.

• A steeper line has a smaller absolute value of slope, indicating a lesser rate of change.

• The slope of a line is unrelated to its steepness.

• A line with zero slope is the steepest line.

What does a positive slope indicate about a linear relationship?

• A positive slope indicates that as x increases, y also increases.

• A positive slope indicates that as x increases, y decreases.

• A positive slope indicates that y remains constant as x increases.

• A positive slope indicates that there is no relationship between x and y.