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 or negative).

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x = 0 and solve for y. The value of y at this point is the y-intercept.

Front

What is the equation of a line with a slope of 2 and a y-intercept of -10?

Back

The equation of the line is y = 2x - 10.

Front

How do you determine if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope (m) is positive and decreasing if the slope is negative.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you convert the slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side.

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept represents the starting value of a situation when x (the independent variable) is zero.

Front

If a linear function has a slope of 0, what does that indicate?

Back

A slope of 0 indicates a horizontal line, meaning that the value of y does not change regardless of the value of x.

Front

How do you find the value of y for a given x in a linear function?

Back

Substitute the value of x into the linear equation and solve for y.