Comparing Linear Functions

Front

What is the slope of a linear function?

Back

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

Front

How do you determine which of two linear equations has a steeper slope?

Back

To determine which of two linear equations has a steeper slope, compare their slope values. The equation with the larger absolute value of the slope is steeper.

Front

What does the y-intercept of a linear function represent?

Back

The y-intercept of a linear function represents the point where the line crosses the y-axis, indicating the value of y when x is zero.

Front

How can you identify the rate of change in a linear function?

Back

The rate of change in a linear function is represented by the slope of the line, indicating how much y changes for a unit change in x.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the difference between positive and negative slopes?

Back

A positive slope indicates that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases.

Front

How do you find the slope from two points on a line?

Back

To find the slope from two points (x1, y1) and (x2, y2), use the formula: slope = (y2 - y1) / (x2 - x1).

Front

What does it mean if two linear equations have the same slope?

Back

If two linear equations have the same slope, they are parallel lines and will never intersect.

Front

What is the significance of the y-intercept in real-world applications?

Back

In real-world applications, the y-intercept can represent an initial value or starting point of a situation, such as the starting amount of money or weight.

Front

How can you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, and use the slope to find another point, then draw a line through the points.