Write Equations from Graphs, Tables, Stories

Front

What is the slope of a linear equation?

Back

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It is calculated as the change in y divided by the change in x (rise over run).

Front

How do you write an equation from a graph?

Back

To write an equation from a graph, identify two points on the line, calculate the slope (m), and use the slope-intercept form y = mx + b, where b is the y-intercept.

Front

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

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

What is the formula for slope (m) between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is a linear equation?

Back

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

Front

How do you determine the equation from a table of values?

Back

To determine the equation from a table, find the rate of change (slope) between the values and use one of the points to find the y-intercept.

Front

What does a negative slope indicate about a graph?

Back

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

Front

What is the significance of the coefficient of x in the equation y = mx + b?

Back

The coefficient of x (m) represents the slope of the line, indicating how much y changes for a unit change in x.

Front

How can you represent a real-world situation with a linear equation?

Back

To represent a real-world situation with a linear equation, identify the variables involved, determine the relationship between them, and express it in the form y = mx + b.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x) has exactly one output (y). A relation can have multiple outputs for a single input.