Linear Functions

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, defined by the equation 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 y-coordinate with respect to the x-coordinate, indicating how steep the line is.

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 slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the y-intercept in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

If a line has a slope of 4, what does this indicate about the line's steepness?

Back

A slope of 4 indicates that for every 1 unit increase in x, the y value increases by 4 units, making the line steep.

Front

What is the equation of a line with a slope of -1 and a y-intercept of 3?

Back

The equation is y = -1x + 3 or y = -x + 3.

Front

How can you determine if two lines are parallel?

Back

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

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.