HCPS: Slope and Y-intercept

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually 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/run).

Front

How do you find the slope from a table of values?

Back

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

Front

What is the y-intercept of a line?

Back

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

Front

How can you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and calculate the slope using the formula: slope (m) = rise/run.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship between the two variables.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 2.

Front

What is the slope of the line represented by the equation y = -3x + 5?

Back

The slope of the line is -3.

Front

How do you determine the slope from two points (1, 2) and (3, 6)?

Back

Using the formula: slope (m) = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the slope of the line if the coordinates of two points are (4, 8) and (4, 10)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.