Comparing Linear Functions

Front

What does the y-intercept of a linear function represent?

Back

The y-intercept represents the value of y when x is 0, often indicating a fixed cost or starting value.

Front

In the equation y = mx + b, what does 'm' represent?

Back

'm' represents the slope of the line, indicating the rate of change of y with respect to x.

Front

What is the slope of the line in the equation y = 2x + 5?

Back

The slope is 2, meaning for every 1 unit increase in x, y increases by 2 units.

Front

How do you determine if one linear function is greater than another?

Back

Compare their slopes and y-intercepts; the function with the greater slope will increase faster.

Front

What does a negative slope indicate about a linear function?

Back

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

Front

If two lines are parallel, what can be said about their slopes?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

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

Back

Rate of change refers to how much y changes for a unit change in x, represented by the slope.

Front

In the context of a real-world problem, what does the y-intercept often represent?

Back

The y-intercept often represents a fixed cost or initial value before any changes occur.

Front

How can you find the equation of a line given its slope and a point on the line?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.