8th Grade 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 dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

How do you calculate the slope between 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 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 is the constant of proportionality?

Back

The constant of proportionality is the constant ratio between two variables that are directly proportional to each other. In a linear function, it is equivalent to the slope.

Front

What does it mean for two quantities to be directly proportional?

Back

Two quantities are directly proportional if they increase or decrease at the same rate, meaning their ratio remains constant.

Front

How can you identify the slope from a table of values?

Back

To identify the slope from a table of values, calculate the change in y divided by the change in x between two points.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent various real-world rates, such as speed, cost per item, or any other rate of change.

Front

What is the formula for the equation of a line in slope-intercept form?

Back

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

Front

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

Back

To find the y-intercept from a linear equation, set x = 0 and solve for y.