Linear MOL 3 Comparing ROC and Initial Value 2019

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope, which indicates how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

How do you determine the initial value in a linear function?

Back

The initial value in a linear function is the y-intercept, which is the value of y when x is 0.

Front

What does the slope of a linear function represent?

Back

The slope represents the steepness of the line and the direction of the relationship between x and y. A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.

Front

If a linear function is represented as y = mx + b, what do m and b represent?

Back

In the equation y = mx + b, m represents the slope of the line, and b represents the y-intercept.

Front

How can you compare the slopes of two linear functions?

Back

To compare the slopes, look at the coefficients of x in their equations. The function with the larger coefficient has a steeper slope.

Front

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

Back

The y-intercept represents the starting value of the dependent variable when the independent variable is zero, often indicating a fixed cost or initial condition.

Front

How do you find the equation of a linear function from a table of values?

Back

To find the equation, determine the slope (rate of change) using two points from the table, then use one point to solve for the y-intercept.

Front

What does it mean if two linear functions have the same slope but different y-intercepts?

Back

It means the functions are parallel; they will never intersect and have the same rate of change.

Front

How do you determine which linear function is cheaper at a given value?

Back

Substitute the value into both functions to find their outputs (costs) and compare the results.

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).