1.8 Interpreting Graphs

Front

What is the slope of a line?

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 change in y divided by the change in x (rise/run).

Front

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

Back

The y-intercept is the point where the line crosses the y-axis. It can be found by setting x = 0 in the equation of the line and solving for y.

Front

What does a positive slope indicate about a line?

Back

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

Front

What is the formula for calculating slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

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

Back

The y-intercept represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

What does it mean if a graph has a slope of 0?

Back

A slope of 0 means the line is horizontal, indicating that y remains constant regardless of the value of x.

Front

What does it mean if a graph has an undefined slope?

Back

An undefined slope occurs in a vertical line, where x remains constant and y changes, indicating no change in x.

Front

How can you describe the motion represented by a graph with a constant slope?

Back

A constant slope indicates uniform motion, meaning the object is moving at a steady speed without acceleration.

Front

What is the relationship between slope and speed in a distance-time graph?

Back

In a distance-time graph, the slope represents speed; a steeper slope indicates a higher speed.