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 much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you find the slope from 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 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.

Front

If a line has a negative slope, what does that indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

What is the initial value in a graph?

Back

The initial value is the value of the dependent variable (y) when the independent variable (x) is 0. It is represented by the y-intercept.

Front

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

Back

A relationship is linear if the rate of change (slope) between any two points is constant.

Front

What does it mean if a line is horizontal?

Back

A horizontal line has a slope of 0, indicating that the dependent variable (y) does not change as the independent variable (x) changes.

Front

What is the formula for 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.