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, indicating 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 point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Write the linear function for a situation where a person saves $50 per month starting with $200.

Back

S(x) = 50x + 200, where S(x) is the total savings after x months.

Front

If a linear function has a slope of 3, what does this mean?

Back

It means that for every 1 unit increase in x, the value of y increases by 3 units.

Front

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

Back

The equation is y = 2x - 3.

Front

How do you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.