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, represented by the coefficient of x in the equation y = mx + b, where m is the slope.

Front

How do you determine which linear equation has a higher slope?

Back

To determine which linear equation has a higher slope, compare the coefficients of x in the equations. The equation with the larger coefficient has the higher slope.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the line crosses the y-axis, represented by the constant term b in the equation y = mx + b.

Front

How can you identify which linear equation has a higher y-intercept?

Back

To identify which linear equation has a higher y-intercept, compare the constant terms in the equations. The equation with the larger constant term has the higher y-intercept.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the value of x increases, the value of y also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, showing an inverse relationship between the two variables.

Front

What is the significance of the slope in real-world applications?

Back

The slope in real-world applications represents the rate of change between two quantities, such as speed, growth rate, or cost per unit.

Front

How do you calculate the slope between two points on a graph?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope, meaning they never intersect and maintain a constant distance apart.