3.1 Equations from a Graph- Math 8

Front

What is the initial value in a graph, and how is it represented?

Back

The initial value is the starting point of the graph, often represented by the y-intercept, which is the value of y when x = 0.

Front

How do you determine the y-intercept from a graph?

Back

The y-intercept can be determined by finding the point where the graph crosses the y-axis.

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change, indicating how much y changes for a unit change in x.

Front

How can you find the slope from two points on a graph?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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

What does a positive slope indicate about a graph?

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 graph?

Back

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

Front

How can you interpret the initial value in a real-world context?

Back

The initial value can represent a starting quantity, such as weight, money, or resources, before any changes occur.

Front

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

Back

The y-intercept often represents the starting point of a scenario, such as initial weight, initial amount of water, or starting distance.

Front

How do you write an equation from a graph?

Back

To write an equation from a graph, identify the slope and y-intercept, then use the slope-intercept form y = mx + b.