Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

How do you determine the steepness of a slope?

Back

The steepness of a slope is determined by the absolute value of the slope (m) in the equation y = mx + b. A larger absolute value indicates a steeper 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. It is represented by the value of b in the equation y = mx + b.

Front

If two linear functions have the same slope, what can be said about their steepness?

Back

If two linear functions have the same slope, they have the same steepness, regardless of their y-intercepts.

Front

What does it mean if a slope is negative?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant of the line.

Front

What does it mean if a slope is positive?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant of the line.

Front

How can you represent a situation with a linear equation?

Back

A situation can be represented with a linear equation by identifying the variables involved and determining the relationship between them, often in the form y = mx + b.

Front

What is the equation of a line with a slope of 3 and a y-intercept of -2?

Back

The equation is y = 3x - 2.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).