Multiple Representations of 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 in a linear relationship?

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

Front

How do you write an equation for a linear relationship?

Back

To write an equation for a linear relationship, identify the slope (m) and the y-intercept (b) from a graph or a set of points, and use the formula y = mx + b.

Front

What is the equation for a candle burning at a rate of 2 inches per hour starting at 7 inches?

Back

y = 7 - 2x, where y is the height of the candle and x is the number of hours burned.

Front

How can you determine the rate of change from a graph?

Back

The rate of change can be determined by calculating the slope of the line on the graph, which is the rise (change in y) over the run (change in x).

Front

What does a negative slope indicate in a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the relationship between the equation y = -1200x and the depth of a submarine?

Back

The equation y = -1200x represents the depth of a submarine descending at a rate of 1200 feet per hour, where y is the depth and x is the time in hours.

Front

How do you interpret the equation y = 425x + 600 in a rental scenario?

Back

In this equation, y represents the total amount paid by tenants, x represents the number of months rented, 425 is the monthly rent, and 600 is the one-time security deposit.

Front

What is the significance of the table corresponding to a linear equation?

Back

A table corresponding to a linear equation shows pairs of values (x, y) that satisfy the equation, illustrating the relationship between the variables.