Writing, Interpreting, & Analyzing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you write an equation for a linear function given a slope and a y-intercept?

Back

The equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

In a real-world context, the y-intercept represents the initial value of the dependent variable before any changes occur.

Front

How can you determine the total cost of items purchased with a linear equation?

Back

The total cost can be modeled with the equation y = mx + b, where m is the cost per item, x is the number of items, and b is any fixed cost.

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

How do you find the value of y for a given x in a linear equation?

Back

Substitute the value of x into the equation and solve for y.

Front

What is the formula to calculate the total savings over time with a fixed monthly deposit?

Back

The total savings can be modeled by the equation y = mx + b, where m is the monthly deposit, x is the number of months, and b is the initial amount.

Front

How do you interpret the solution of a linear equation in a real-world scenario?

Back

The solution represents the value of the dependent variable (y) based on the given value of the independent variable (x) in a specific context.