Slope and Graphing

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically 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 calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

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

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, where the x-values are constant and the y-values can vary.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that the y-values remain constant as the x-values change.

Front

How can you determine if a point is a solution to a system of equations?

Back

A point (x, y) is a solution to a system of equations if it satisfies all equations in the system when substituted into them.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the equation y = mx + b.

Front

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

Back

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

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 divide rise by run.