8.4C: Slope and Y-Intercept

Front

What does the variable 'b' represent in the slope-intercept form of a linear equation, y = mx + b?

Back

The variable 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

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

Back

'm' represents the slope of the line, indicating the steepness and direction of the line.

Front

How do you calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of the line represented by the equation y = 2x - 4?

Back

The y-intercept is -4, which means the line crosses the y-axis at the point (0, -4).

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line is decreasing; for every 1 unit increase in x, y decreases by 3 units.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, meaning there is no change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

If the slope of a line is 1/2, what does this mean in terms of rise over run?

Back

It means that for every 2 units you move to the right (run), the line rises 1 unit (rise).

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 use the formula m = rise/run.

Front

What does it mean if a line has a positive slope?

Back

A positive slope means that as x increases, y also increases, indicating an upward trend.