Slope and y-intercept

Front

What is the definition of slope in a linear function?

Back

The slope of a linear function is a measure of the steepness of the line, represented by 'm' in the equation y = mx + b. It indicates the change in y for a unit change in x.

Front

How is the slope calculated 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 the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the coordinate (0, b) in the equation y = mx + b.

Front

In the equation y = mx + b, what does 'b' represent?

Back

In the equation y = mx + b, 'b' represents the y-intercept of the line.

Front

What is the slope of a line that rises 3 units for every 2 units it runs to the right?

Back

The slope of the line is 3/2.

Front

If a line has a slope of -1/2, what does this indicate about its direction?

Back

A slope of -1/2 indicates that the line descends from left to right, meaning for every 2 units moved to the right, the line moves down 1 unit.

Front

How can you identify the slope from a graph of a linear function?

Back

The slope can be identified by selecting two points on the line and calculating the rise over run (change in y over change in x).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would involve division by zero (change in x is 0).

Front

How do you find the y-intercept from a graph?

Back

The y-intercept can be found by locating the point where the line crosses the y-axis.