Multiple representations 7.4A, 7.7A

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in 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 y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you interpret the equation y = 2x + 3?

Back

In this equation, the slope is 2, meaning for every 1 unit increase in x, y increases by 2 units. The y-intercept is 3, meaning the line crosses the y-axis at (0, 3).

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

How can you represent a relationship using a table?

Back

A table can show pairs of values (x, y) that represent the relationship between two variables. Each row corresponds to a specific input-output pair.

Front

What is the purpose of graphing a linear equation?

Back

Graphing a linear equation visually represents the relationship between variables, making it easier to understand and analyze.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line when graphed.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points, calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), then use one of the points to solve for the y-intercept (b).

Front

What is a table of values?

Back

A table of values lists pairs of x and y values that satisfy a particular equation, helping to visualize the relationship.