Linear Functions (A1.2.1.2.1)

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 (m) of a linear function represents the rate of change of the function. 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 (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

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

Back

Substitute the value of x into the linear function equation y = mx + b and solve for y.

Front

What does the point (x,y) represent on the graph of a linear function?

Back

The point (x,y) represents a specific input-output pair, where x is the independent variable and y is the dependent variable.

Front

How can 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.

Front

What does the equation y = 3x + 5 represent?

Back

This equation represents a linear function with a slope of 3 and a y-intercept of 5.

Front

If a cyclist travels according to the function y = 16x + 8, how far will she be after 3 hours?

Back

After 3 hours, she will be 56 miles from her home.

Front

What does the point (20,55) mean in the context of a weight vs. volume graph?

Back

It means that twenty gallons of water weighs 55 pounds.

Front

How do you interpret the coordinate (2,3) on a height vs. days graph?

Back

It means that after 2 days, the plant will be 3 cm tall.