2.1.2 Slope from a Graph

Front

What is 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.

Front

How do you calculate the slope from two points?

Back

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

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 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

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of 'b' in the slope-intercept form.

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 and using the rise over run method: rise (change in y) over run (change in x).

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 is the significance of an undefined slope?

Back

An undefined slope indicates a vertical line, where the x-value remains constant while the y-value changes.

Front

How does the slope affect the angle of a line?

Back

The slope of a line affects its angle with the horizontal axis; a steeper slope corresponds to a larger angle.