Writing Linear Equations (Rate of Change and Initial Value)

Front

What is the initial value in a linear equation, and how is it represented?

Back

The initial value in a linear equation is the y-intercept, which represents the value of y when x is 0. It is often denoted as 'b' in the equation y = mx + b.

Front

How do you identify the rate of change in a linear function?

Back

The rate of change in a linear function is the slope (m) of the line, which indicates how much y changes for a unit change in x.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

In the equation y = 2x + 13, what is the slope and what does it represent?

Back

In the equation y = 2x + 13, the slope is 2, which means for every 1 unit increase in x, y increases by 2 units.

Front

What does a negative slope indicate in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

How can you determine if a linear equation is correctly representing a real-world situation?

Back

You can determine if a linear equation correctly represents a real-world situation by checking if the initial value and rate of change align with the context of the problem.

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept represents the starting point or initial condition of the situation being modeled, such as the initial amount before any changes occur.

Front

How do you convert a linear equation from one form to another, such as from slope-intercept to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to isolate the variables on one side.

Front

What is the relationship between the slope and the rate of change in a linear function?

Back

The slope of a linear function is the same as the rate of change; it quantifies how much the dependent variable (y) changes with respect to the independent variable (x).

Front

How can you verify if a given equation accurately represents a situation described in a problem?

Back

You can verify if a given equation accurately represents a situation by substituting known values from the problem into the equation and checking if the outputs match the expected results.