8th Grade Unit 3 IM

Front

What is the rate of change in a linear relationship?

Back

The rate of change in a linear relationship is the constant amount that the dependent variable changes for each unit change in the independent variable, often represented as the slope of the line.

Front

How do you determine the slope of a line from an equation?

Back

The slope of a line in the equation y = mx + b is represented by 'm'. It indicates the steepness and direction of the line.

Front

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

Back

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

Front

How can you write an equation from a word problem involving a fixed income and variable expenses?

Back

Identify the fixed income as the starting point and subtract the variable expenses multiplied by the number of occurrences to form the equation: y = fixed income - (variable expense * x).

Front

What is the formula to find the total amount of water in a tank before it was drained?

Back

The total amount of water in the tank can be found by adding the amount drained to the amount left in the tank.

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed, typically in the form y = mx + b.

Front

How do you interpret the meaning of a negative slope in a linear equation?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases, showing an inverse relationship.

Front

What is the significance of the constant term in a linear equation?

Back

The constant term in a linear equation represents the y-intercept, which is the value of y when x is zero.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points, calculate the slope (m) using the formula (y2 - y1) / (x2 - x1) and then use the point-slope form y - y1 = m(x - x1) to derive the equation.

Front

What is the relationship between the slope and the rate of change in a real-world context?

Back

In real-world contexts, the slope represents the rate of change, indicating how one quantity changes in relation to another.