8th STAAR 4c (ID slope and y-intercept)

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the change in y (rise) divided by the change in x (run).

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It can be found by setting x = 0 in the equation of the line.

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 calculating slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

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

Back

The y-intercept represents the starting value of y when x is zero, often indicating an initial condition in real-world scenarios.

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 then divide rise by run.

Front

What does the slope represent in a real-world scenario, such as speed?

Back

In a scenario like speed, the slope represents the rate of change, such as distance per unit of time (e.g., miles per hour).

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you interpret the slope in a profit vs. number of items sold graph?

Back

The slope represents the profit made per item sold; a steeper slope indicates higher profit per item.