Linear Functions

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. 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, indicating how much the output (y-value) changes for a given change in the input (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, represented by the value of y when x = 0.

Front

What is the difference between input and output in a function?

Back

Input refers to the value you provide to the function (x-value), while output is the value the function returns (y-value).

Front

What is the definition of a function?

Back

A function is a relation where each input has exactly one output.

Front

If the slope of a line is 2, what does this mean?

Back

It means that for every 1 unit increase in x, the value of y increases by 2 units.

Front

How do you find the output value of a linear function?

Back

To find the output value, substitute the input value into the function's equation and solve for y.

Front

What is the equation of a line with a slope of 3 and a y-intercept of -2?

Back

The equation is y = 3x - 2.

Front

What does it mean if a linear function has a slope of 0?

Back

A slope of 0 means the line is horizontal, indicating that the output value does not change regardless of the input.

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).