Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented by the letter m in the equation of a line. It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you determine if a graph is linear?

Back

A graph is linear if it forms a straight line. This can be determined by checking if the relationship between the x and y coordinates is consistent and can be expressed in the form y = mx + b.

Front

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

Back

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

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that if one line has a slope of m, the other line must have a slope of -1/m.

Front

How do you find the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For linear functions, the domain is usually all real numbers.

Front

How do you find the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For linear functions, the range is usually all real numbers.

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. It is represented by the value of b in the slope-intercept form y = mx + b.

Front

How do you write the equation of a line given two points?

Back

To write the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to find the equation.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.