Writing Linear Equations (Rate of Change and Initial Value)

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line when graphed. It can be written in the form y = mx + b, where m is the slope (rate of change) and b is the y-intercept (initial value).

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) 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 unit change in x.

Front

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

Back

The y-intercept (b) represents the initial value of the dependent variable (y) when the independent variable (x) is zero. It is the point where the line crosses the y-axis.

Front

How do you determine the initial value from a linear equation?

Back

The initial value can be determined by identifying the y-intercept (b) in the equation y = mx + b.

Front

What is the rate of change in the context of a linear equation?

Back

The rate of change is the slope (m) of the linear equation, indicating how much the dependent variable (y) changes for each unit increase in the independent variable (x).

Front

If a linear equation is given as y = 4x + 10, what is the initial value?

Back

The initial value is 10, which is the y-intercept of the equation.

Front

If a linear equation is y = -3x + 5, what does the negative slope indicate?

Back

The negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

How can you verify if a linear equation accurately represents a situation?

Back

You can verify by checking if the initial value and rate of change match the context of the situation described.

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

In the equation y = 5x - 7, what is the rate of change?

Back

The rate of change is 5.