Slope and Y-intercept

Front

What is the definition of the slope of a line?

Back

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

Front

What is the y-intercept of a line?

Back

The y-intercept of a line is the point where the line crosses the y-axis. It is represented as 'b' in the slope-intercept form of a linear equation (y = mx + b).

Front

How do you find the slope from two points on a line?

Back

To find the slope (m) from two points (x1, y1) and (x2, y2), use the formula: m = (y2 - y1) / (x2 - x1).

Front

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

Back

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

Front

How can you identify the slope from a graph?

Back

The slope can be identified from a graph by selecting two points on the line, calculating the rise (vertical change) and run (horizontal change) between them, and then using the formula slope = rise/run.

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, 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-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the significance of a slope of zero?

Back

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

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x remains constant while y changes, resulting in a division by zero in the slope formula.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.