7.7A 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 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 write an equation from a word problem involving a linear relationship?

Back

Identify the variables, determine the rate of change (slope), and the starting value (y-intercept), then use the slope-intercept form y = mx + b.

Front

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

Back

The equation is y = 2x + 3.

Front

If a line has a slope of -1, what does this indicate about the relationship between x and y?

Back

A slope of -1 indicates that as x increases, y decreases at the same rate.

Front

What does it mean for two variables to be directly proportional?

Back

Two variables are directly proportional if they increase or decrease together at a constant rate, represented by a linear equation through the origin (0,0).

Front

How can you determine the equation of a line from a graph?

Back

Identify two points on the line, calculate the slope (rise over run), and use one of the points to find the y-intercept.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the relationship between the coefficients in the equation y = mx + b and the graph of the line?

Back

The coefficient m represents the slope of the line, while b represents the y-intercept, determining where the line crosses the y-axis.