Writing, Interpreting, & Analyzing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

What is the y-intercept in a linear function?

Back

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

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 does it mean if the slope is negative in a linear function?

Back

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

Front

How can you determine the slope from two points on a line?

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 significance of the y-intercept in real-world problems?

Back

The y-intercept often represents the starting value or initial condition of a situation before any changes occur.

Front

How do you interpret the meaning of a linear equation in a real-world context?

Back

You can interpret a linear equation by identifying the variables, understanding the slope as a rate of change, and the y-intercept as the starting point.

Front

What is the equation of a line with a slope of -2 and a y-intercept of 120?

Back

The equation is y = -2x + 120.

Front

If a function has a slope of 24, what does this indicate in a practical scenario?

Back

It indicates that for every unit increase in x, the value of y increases by 24 units.