Analyzing Linear Equations

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise over run).

Front

How do you find the slope using a table of values?

Back

To find the slope using a table, select two points (x1, y1) and (x2, y2) from the table. The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does the 'b' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

What is a y-intercept?

Back

The y-intercept is the value of y when x is 0. It indicates where the line intersects the y-axis.

Front

True or False: The ordered pairs in a linear equation will always create a straight line when plotted.

Back

True.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a set of points forms a linear relationship?

Back

A set of points forms a linear relationship if they can be connected by a straight line when plotted on a graph.

Front

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

Back

The slope indicates the rate of change between two variables. For example, in a distance-time graph, the slope represents speed.

Front

How do you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the formula m = rise/run.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.