Unit 4: Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of 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 and the direction it goes (upward or downward).

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 in a linear equation?

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 does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in the y-value as the x-value changes.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing, meaning as the x-value increases, the y-value decreases.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right.

Front

How can you determine if a relationship is linear from a table of values?

Back

A relationship is linear if the differences between the y-values are constant for equal intervals of x-values.

Front

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

Back

The equation of the line is y = 2x + 3.