Linear Relationships Prep

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 is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities. In the equation y = kx, k represents the constant of proportionality.

Front

How do you find the constant of proportionality from a word problem?

Back

To find the constant of proportionality, divide the dependent variable (y) by the independent variable (x) for any pair of values. For example, if 14 gallons of gas cost $48.86, the constant of proportionality is $48.86 / 14.

Front

What does the slope of a linear equation represent?

Back

The slope of a linear equation 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 in the equation of a line. It represents the point where the line crosses the y-axis.

Front

How can you determine if a relationship is proportional?

Back

A relationship is proportional if the ratio of the dependent variable to the independent variable is constant. This means that the graph of the relationship will pass through the origin (0,0).

Front

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

Back

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

If the equation of a line is y = 3x + 4, what is the slope?

Back

The slope of the line y = 3x + 4 is 3.

Front

If a table shows a nonproportional relationship, what does that mean?

Back

A nonproportional relationship means that the ratio of the dependent variable to the independent variable is not constant. The graph will not pass through the origin.

Front

How do you extend a linear relationship in a table?

Back

To extend a linear relationship in a table, use the equation of the line to calculate the dependent variable (y) for new values of the independent variable (x).