A.3A, A.3B: Finding slope and rate of change from a Graph

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness of a line, calculated as the change in y (rise) divided by the change in x (run).

Front

How do you calculate the rate of change from a graph?

Back

Rate of change is calculated by taking the change in the y-values divided by the change in the x-values (Δy/Δx).

Front

What does a slope of 1/2 indicate about a line?

Back

A slope of 1/2 indicates that for every 1 unit increase in x, the y value increases by 0.5 units.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x value increases, the y value decreases.

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

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, indicating the value of y when x is 0.

Front

If a line has a slope of 0, what does this mean?

Back

A slope of 0 means the line is horizontal, indicating no change in y as x changes.

Front

What does it mean if a line is vertical in terms of slope?

Back

A vertical line has an undefined slope because the change in x is 0, leading to division by zero.

Front

How can you visually identify the slope of a line on a graph?

Back

The slope can be visually identified by the steepness of the line; steeper lines have greater slopes.

Front

What is the relationship between slope and rate of change?

Back

Slope is a specific type of rate of change that describes how much y changes for a given change in x.