Lesson 9 Flashcard

Front

What is the definition of slope in a graph?

Back

The slope is a measure of the steepness of a line, calculated as the change in the y-value divided by the change in the x-value.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases.

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope is calculated using the formula: slope = (y2 - y1) / (x2 - x1).

Front

If a tank is losing water at a rate of 60 gallons per hour, what is the slope of the function representing this situation?

Back

The slope is -60, representing the rate at which the amount of water decreases.

Front

What does the initial value of a function represent?

Back

The initial value represents the starting point of the function, often the y-value when x is 0.

Front

In the equation slope = (y2 - y1) / (x2 - x1), what do y2 and y1 represent?

Back

y2 and y1 represent the y-values of two different points on the graph.

Front

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

Back

The y-intercept can represent the starting amount of a quantity before any changes occur.

Front

If a tree grows from 4 feet to 8 feet over 4 years, what is the slope of the growth?

Back

The slope is 1 foot per year, calculated as (8 - 4) / (4 - 0).

Front

What does it mean if the slope of a line is zero?

Back

A slope of zero means that the line is horizontal, indicating no change in the y-value as the x-value changes.