Multiple Representations

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 (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you interpret the equation y = 3x + 4?

Back

In this equation, for every increase of 1 in x, y increases by 3. The line crosses the y-axis at 4.

Front

What is the difference between dependent and independent variables?

Back

The independent variable is the input (x), while the dependent variable is the output (y) that depends on the value of x.

Front

What does the equation y = 20x + 120 represent in a real-world context?

Back

This equation could represent a bank account where $120 is the initial deposit and $20 is added each week.

Front

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

Back

To determine the equation, identify the slope (rise over run) and the y-intercept from the graph.

Front

What does it mean if a linear equation has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward sloping line.

Front

What is the significance of the equation y = 3x + 4 in a word problem?

Back

This equation can represent a situation where a fixed cost of 4 is added to a variable cost that increases by 3 for each unit of x.

Front

How do you write an equation from a word problem?

Back

Identify the fixed and variable components, assign variables to them, and express their relationship in an equation.