Slope and Slope Intercept Form

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How is slope calculated between two points (x1, y1) and (x2, y2)?

Back

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-value increases, the y-value also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant from left to right.

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

What does 'b' represent in the slope-intercept form of a linear equation?

Back

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

Front

How can you determine the slope from a graph?

Back

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

Back

The y-intercept is significant because it indicates the value of y when x is zero, providing a starting point for the line on the graph.

Front

How do you find the slope of a line given two points?

Back

To find the slope, use the formula m = (y2 - y1) / (x2 - x1) with the coordinates of the two points.

Front

What type of slope does a horizontal line have?

Back

A horizontal line has a slope of 0, indicating no vertical change as x changes.