Linear Relationships Review

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 expressed in the form of an equation, typically 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 one-unit increase in x.

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 the value of y when x is 0, represented by the 'b' in the equation y = mx + b.

Front

How do you identify the origin on a graph?

Back

The origin is the point where the x-axis and y-axis intersect, represented by the ordered pair (0,0).

Front

What is the equation for a situation where a fixed cost of $4 is added to a variable cost of $3 per child?

Back

The equation is y = 3x + 4, where y is the total cost and x is the number of children.

Front

What does the term 'ordered pair' mean in graphing?

Back

An ordered pair is a pair of numbers used to locate a point on a graph, written in the form (x, y), where x is the horizontal coordinate and y is the vertical coordinate.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the variable that is changed or controlled in an experiment, while the dependent variable is the variable that is measured or affected.

Front

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

Back

A relationship is linear if the change in y divided by the change in x (the slope) is constant for all pairs of values.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does it mean if a line has a positive slope?

Back

A line with a positive slope rises from left to right, indicating that as the independent variable (x) increases, the dependent variable (y) also increases.