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 expressed in the form of an equation, typically written as 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 equation?

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 can you represent a linear relationship using a table?

Back

A linear relationship can be represented using a table that shows pairs of values for the independent variable (x) and the dependent variable (y). Each pair should satisfy the linear equation.

Front

What is the equation for calculating total earnings based on hourly wage and hours worked?

Back

The equation is W = rt, where W is total earnings, r is the hourly wage, and t is the number of hours worked.

Front

How do you graph a linear equation?

Back

To graph a linear equation, you can plot points that satisfy the equation and then connect them with a straight line. Alternatively, you can use the slope and y-intercept to draw the line.

Front

What does the equation y = -1.5x + 12 represent in a real-world context?

Back

This equation represents a candle that starts at 12 inches and burns down at a rate of 1.5 inches per hour. The variable x represents time in hours, and y represents the remaining height of the candle.

Front

What is the significance of the negative slope in the equation y = -1200x?

Back

The negative slope indicates that the value of y (depth) decreases as x (time) increases, meaning the submarine is descending deeper into the water.

Front

How can you determine the total amount in a savings account after a certain number of months?

Back

You can determine the total amount using the equation t = pm + P, where t is the total amount, p is the monthly deposit, m is the number of months, and P is the initial amount.

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y) for each input (x). In the context of linear relationships, it can be represented as an equation.