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 the y-value with respect to the x-value. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you find 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 can be found by setting x = 0 in the equation of the line.

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

If a line has a positive slope, what does that indicate about the line's direction?

Back

A line with a positive slope rises from left to right.

Front

If a line has a negative slope, what does that indicate about the line's direction?

Back

A line with a negative slope falls from left to right.

Front

What is the y-intercept of the equation y = 3x + 5?

Back

The y-intercept is 5.

Front

How do you write the equation of a line given a slope and a y-intercept?

Back

Use the slope-intercept form: y = mx + b, substituting m for the slope and b for the y-intercept.

Front

What is the slope of the line represented by the equation y = -2x + 4?

Back

The slope is -2.

Front

What does it mean if two lines are parallel?

Back

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