Write Equations from Graphs, Tables, Stories

Front

What is the initial value (y-intercept)?

Back

The initial value (y-intercept) is the value of y when x is 0. It represents the starting point of a linear relationship.

Front

What is the rate of change (slope)?

Back

The rate of change (slope) indicates how much y changes for a unit change in x. It is calculated as the rise over run.

Front

How do you determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, identify the slope and y-intercept, then use the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

In a real-world context, the slope represents the rate at which one quantity changes in relation to another, such as speed or cost per item.

Front

What is the formula for calculating slope?

Back

The formula for calculating slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b.

Front

What does the y-intercept tell us in a story problem?

Back

The y-intercept in a story problem indicates the starting value or initial condition before any changes occur.

Front

How can you write an equation from a table of values?

Back

To write an equation from a table of values, identify the slope and y-intercept from the data points, then use the linear equation format.

Front

What is the significance of the x-value in a linear equation?

Back

The x-value in a linear equation represents the independent variable, which can be manipulated to observe changes in the dependent variable (y).

Front

What is the difference between a positive and negative slope?

Back

A positive slope indicates that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases.