Multiple Representations of 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 line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept of 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

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

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

Back

The equation of the line is y = 2x + 3.

Front

How can you represent a linear function using a table?

Back

A linear function can be represented in a table by listing pairs of x and y values that satisfy the function's equation.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Front

How can you convert a verbal description into a linear equation?

Back

To convert a verbal description into a linear equation, identify the slope and y-intercept from the context of the description.

Front

What is the significance of the equation y = 0?

Back

The equation y = 0 represents a horizontal line that intersects the x-axis at all points.