Slope and Y-Intercept

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on the line.

Front

How do you calculate the slope 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 a positive slope indicate about a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no change in the y-coordinate as the x-coordinate changes.

Front

What is the slope of a vertical line?

Back

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

Front

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

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

How can you find the y-intercept from the slope-intercept form of a line?

Back

In the slope-intercept form of a line (y = mx + b), the y-intercept is the value of 'b' when x = 0.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept indicates the starting value of y when x is zero, providing a reference point for the line on the graph.

Front

How do you interpret a slope of 0 in a real-world context?

Back

A slope of 0 indicates that there is no change in the dependent variable regardless of changes in the independent variable, suggesting a constant value.