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 y with respect to x. It indicates how steep the line is and the direction it goes (positive slope means the line rises, negative slope means it falls).

Front

How do you find the slope from an equation in slope-intercept form?

Back

In the slope-intercept form y = mx + b, the slope is the coefficient m of x.

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 b in the equation y = mx + b.

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the difference between a positive and negative slope?

Back

A positive slope indicates that as x increases, y also increases. A negative slope indicates that as x increases, y decreases.

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 (i.e., the slopes are negative reciprocals of each other).

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 x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.