Comparing 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 dependent variable (y) changes for a unit change in the independent variable (x).

Front

How do you find 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 y-intercept in a linear function?

Back

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

Front

How can you determine if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope (m) is positive and decreasing if the slope is negative.

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

If a rental cost is represented by y = 400x + 600, what does 400 represent?

Back

The 400 represents the monthly rental cost per tenant.

Front

What does the term 'rate of change' refer to in a linear function?

Back

The rate of change refers to how much the output (y) changes for a unit change in the input (x), which is represented by the slope.

Front

How do you compare two linear functions to determine which is cheaper?

Back

To compare two linear functions, evaluate both functions at the same value of x and compare the resulting y values.

Front

What is the significance of the constant term in a linear equation?

Back

The constant term (b) in the equation y = mx + b represents the y-intercept, which is the starting value of y when x is 0.