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 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 do you identify a linear equation from a table of values?

Back

A linear equation can be identified from a table of values if the differences between consecutive y-values are constant when the x-values increase by the same amount.

Front

What is the equation for finding the cost of downloading n songs at $0.99 each?

Back

t = 0.99n, where t is the total cost and n is the number of songs.

Front

What does it mean for y to be a function of x?

Back

It means that for every value of x, there is exactly one corresponding value of y. In other words, each input (x) has a unique output (y).

Front

What is the difference between dependent and independent variables?

Back

The independent variable is the variable that is changed or controlled in an experiment (usually x), while the dependent variable is the variable that is measured or affected (usually y).

Front

How can you determine if a point (x, y) lies on the line represented by a linear equation?

Back

To determine if a point (x, y) lies on the line, substitute the x-value into the equation and see if the resulting y-value matches the y-value of the point.

Front

What is the significance of the equation y = 2x?

Back

The equation y = 2x indicates that for every unit increase in x, y increases by 2 units. This shows a direct proportional relationship with a slope of 2.

Front

What does the equation y = x + 2 represent?

Back

The equation y = x + 2 represents a linear relationship where the y-value is always 2 more than the x-value. The slope is 1 and the y-intercept is 2.