CC3 (Ch. 4) 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?

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 graph?

Back

A linear equation can be identified from a graph if the points form a straight line. You can also find the slope and y-intercept from the graph.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation of the line is y = 2x + 3.

Front

If a line passes through the points (1, 2) and (3, 6), what is the slope?

Back

The slope (m) is calculated as (y2 - y1) / (x2 - x1) = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What does it mean for two quantities to be proportional?

Back

Two quantities are proportional if they maintain a constant ratio. In a graph, this is represented by a straight line that passes through the origin.

Front

Write the equation for a situation where a person earns $50 for every 4 hours worked.

Back

The equation is y = 12.5x, where y is the total earnings and x is the number of hours worked.

Front

What is the difference between dependent and independent variables?

Back

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

Front

How can you determine the next values in a linear sequence?

Back

To determine the next values in a linear sequence, identify the common difference between consecutive terms and add it to the last term.