Linear Functions Flashcard

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

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

Back

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

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

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

Back

The equation is y = 2x + 3.

Front

If a line has a slope of -1, what does this indicate about the line's direction?

Back

A slope of -1 indicates that the line descends from left to right.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) represents the y-intercept of the line, where the line crosses the y-axis.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the formula for writing the equation of a line given a point and a slope?

Back

The equation can be written using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What does it mean if a line has a slope of 0?

Back

A slope of 0 means the line is horizontal and does not rise or fall as it moves along the x-axis.