Interpret Rate of Change and Initial Value from a Table

Front

What is the rate of change in a linear equation?

Back

The rate of change in a linear equation represents how much the dependent variable (y) changes for a unit change in the independent variable (x). It is the slope of the line.

Front

What does the initial value represent in a linear equation?

Back

The initial value in a linear equation is the value of y when x is 0. It is also known as the y-intercept.

Front

How do you write an equation from a table of values?

Back

To write an equation from a table, identify the rate of change (slope) and the initial value (y-intercept) and use the slope-intercept form: y = mx + b.

Front

What is the slope of the line represented by the equation y=6.25x+65?

Back

The slope of the line is 6.25.

Front

If $250 is deposited per month, what is the initial value after 0 months?

Back

The initial value is $500.

Front

What does a constant rate of change indicate about a relationship?

Back

A constant rate of change indicates a linear relationship between the variables.

Front

How can you determine the y-intercept from a table?

Back

The y-intercept can be determined by finding the value of y when x is 0.

Front

What does a rate of change of 1120 ft/min represent in a cycling scenario?

Back

It represents the constant speed at which the cyclist is riding.

Front

What is the formula for slope given two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

In the equation y = mx + b, what does 'b' represent?

Back

'b' represents the y-intercept, or the initial value when x = 0.