Slope from a Graph Practice

Front

What is the definition of slope in the context of a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope of a line given 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 negative slope indicate about a graph?

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 does a positive slope indicate about a graph?

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 is the unit rate in the context of slope?

Back

The unit rate is the slope of a line that represents the amount of change in the dependent variable for a one-unit change in the independent variable.

Front

How can you interpret the slope of a graph in a real-world context?

Back

The slope can represent rates of change, such as speed, growth rate, or any other quantity that changes over time or another variable.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of the dependent variable when the independent variable is zero.

Front

How does the slope relate to the rate of descent or ascent in real-world scenarios?

Back

The slope represents the rate of descent (negative slope) or ascent (positive slope) in real-world scenarios, such as diving, climbing, or filling a container.

Front

What is the relationship between the slope of a line and the speed of an object in motion?

Back

The slope of a line on a distance-time graph represents the speed of an object; a steeper slope indicates a higher speed.

Front

How can you determine if a graph represents a constant rate of change?

Back

A graph represents a constant rate of change if it is a straight line, indicating that the slope remains the same throughout.