8th Linear Functions (8.F.B.4) Flashcard

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, defined by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the rate of change represent in a linear function?

Back

The rate of change in a linear function represents the slope (m) of the line, indicating how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

How do you determine the constant of proportionality from a table of values?

Back

The constant of proportionality can be determined by finding the ratio of the dependent variable to the independent variable for any pair of values in the table, provided the relationship is linear.

Front

What is the explicit formula for a linear sequence?

Back

The explicit formula for a linear sequence can be expressed as a_n = a + d(n - 1), where a is the first term, d is the common difference, and n is the term number.

Front

How can you write an equation for a real-world scenario involving growth?

Back

To write an equation for a real-world scenario involving growth, identify the initial value and the rate of change, then use the formula y = mx + b, where m is the rate of change and b is the initial value.

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

How do you find the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept (b) is the value of y when x is 0, representing the starting point of the function on the y-axis.

Front

How can you identify a linear relationship from a graph?

Back

A linear relationship can be identified from a graph if the plotted points form a straight line.

Front

What is the difference between proportional and non-proportional relationships?

Back

In a proportional relationship, the ratio of the dependent variable to the independent variable is constant, while in a non-proportional relationship, this ratio varies.