Topic 4 Review: 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 does it mean for y to vary inversely with x?

Back

If y varies inversely with x, it means that as x increases, y decreases, and vice versa. This relationship can be expressed as y = k/x, where k is a constant.

Front

If y = 150 when x = 2, what is the value of y when x = 25?

Back

y = 12.

Front

What is the equation of a line with a slope of 1/3 and a y-intercept of -2?

Back

y = 1/3x - 2.

Front

What type of variation is represented by the equation y = k/x?

Back

Inverse variation.

Front

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

Back

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

Front

What is the y-intercept in the equation y = 4/5x + 4?

Back

The y-intercept is 4.

Front

What is the slope of the line represented by the equation y = -3x - 2?

Back

The slope is -3.

Front

How can you determine if a relationship is direct or inverse variation?

Back

If y increases as x increases, it is direct variation. If y decreases as x increases, it is inverse variation.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.