Writing Linear Functions

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 the y-value with respect to the x-value. 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

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant of the line.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -1/m.

Front

Write the equation of a line with a slope of 2 and a y-intercept of -3.

Back

y = 2x - 3.

Front

What is the slope of a line that is perpendicular to y = 4x + 1?

Back

The slope of the perpendicular line is -1/4.