y = mx + b, interpreting m and b, and systems of equations

Front

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

Back

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

Front

What does the slope (m) represent in the equation y = mx + b?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

Is the equation y = 25x - 15 proportional?

Back

No, because it has a non-zero y-intercept (-15), which means it does not pass through the origin.

Front

Write a linear equation for an airplane descending at 2,000 feet per minute from 30,000 feet.

Back

y = -2000x + 30000

Front

What does a negative slope indicate in a linear equation?

Back

A negative slope indicates that as x increases, y decreases.

Front

What is the general form of a linear equation?

Back

The general form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If a plane's height is represented by y and time by x, what does the equation y = -2000x + 30000 tell us?

Back

It tells us that the plane starts at 30,000 feet and descends at a rate of 2,000 feet per minute.

Front

What is the x-intercept in a linear equation?

Back

The x-intercept is the value of x when y is 0, indicating where the line crosses the x-axis.

Front

How do you determine if a linear equation is proportional?

Back

A linear equation is proportional if it can be written in the form y = mx, meaning it has a slope but no y-intercept (b = 0).

Front

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

Back

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