Comparing Linear Functions

Front

What is the definition of slope in a linear function?

Back

The slope is a measure of the steepness of a line, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

How do you determine which linear function has a greater slope?

Back

Compare the slope values (coefficients of x) of the functions. The function with the larger slope value has a greater slope.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

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

Back

A slope of 0 means the line is horizontal, indicating that the y-value does not change as the x-value changes.

Front

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

Back

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

Front

In the context of a real-world scenario, what does the slope represent?

Back

The slope represents the rate of change or the cost per unit in a real-world context, such as cost per hour or price per item.

Front

How can you visually compare the slopes of two linear functions on a graph?

Back

By plotting both lines on the same graph, you can visually assess which line is steeper (greater slope) and which is flatter (lesser slope).

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you find the y-intercept from the slope-intercept form of a linear equation?

Back

In the slope-intercept form y = mx + b, 'b' represents the y-intercept.