Unit 2 Flashcard

Front

What is the y-intercept of the equation 6x + 3y = -12?

Back

The y-intercept is the point where the line crosses the y-axis. For the equation 6x + 3y = -12, the y-intercept is (0, -4).

Front

How do you determine the equation of a line from a graph showing a constant rate of change?

Back

The equation can be determined using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. For example, if the graph shows a slope of 3 and a y-intercept of 18, the equation is y = 3x + 18.

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change. For example, in a snowstorm, if the slope is 3, it means that for every hour, 3 inches of snow falls.

Front

What does the flat fee in a linear function represent?

Back

The flat fee represents the y-intercept in the equation of the function. For example, in the kayak rental scenario, the flat fee is $10.

Front

If x = -3 in the equation 6x + 3y = -12, what is the value of y?

Back

Substituting x = -3 into the equation gives 6(-3) + 3y = -12, which simplifies to 3y = 6, so y = 2.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) represents the y-intercept, which is the value of y when x is 0.

Front

How can you find the total cost of renting a kayak for a certain number of hours?

Back

The total cost can be calculated using the equation C = mx + b, where m is the hourly rate, x is the number of hours, and b is the flat fee.

Front

What does it mean if a graph is linear?

Back

A linear graph indicates a constant rate of change, meaning the relationship between the variables can be expressed with a linear equation.

Front

What is the formula for slope in a linear equation?

Back

The slope (m) is calculated as the change in y divided by the change in x (m = Δy/Δx).

Front

What does the term 'constant rate' imply in a mathematical context?

Back

A constant rate implies that the change in one variable is consistent with the change in another variable over time.