8th Unit 3 Lesson 5: Intro to Linear

Front

What is the slope/rate of change in a linear function?

Back

The slope (m) represents the rate of change of the function, indicating how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0, representing the starting point of the line on the graph.

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

What is the formula for a linear equation in slope-intercept form?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and use the formula slope = rise/run.

Front

What is the significance of the constant rate of change in real-world applications?

Back

The constant rate of change helps in understanding relationships such as speed, cost per unit, and other linear relationships in real-world scenarios.

Front

How do you interpret the slope in a real-world context?

Back

The slope can represent rates such as speed (distance over time) or cost (cost per item), providing insight into how one variable affects another.