Comparing Linear Functions

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 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

How do you determine the y-intercept of a linear equation?

Back

The y-intercept of a linear equation is the value of y when x is 0. It can be found by substituting x = 0 into the equation.

Front

What is the difference between the slopes of two linear functions?

Back

The difference between the slopes of two linear functions indicates which function is increasing or decreasing faster. A larger slope means a steeper increase.

Front

How can you compare the y-intercepts of two linear equations?

Back

To compare the y-intercepts of two linear equations, evaluate each equation at x = 0 and compare the resulting y values.

Front

What does it mean if two linear functions have the same y-intercept?

Back

If two linear functions have the same y-intercept, it means they intersect the y-axis at the same point, but they may have different slopes.

Front

What is the significance of a negative slope in a linear function?

Back

A negative slope indicates that as x increases, y decreases. This represents a decreasing linear relationship.

Front

How do you find the slope of a line given two points?

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 standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you graph a linear function?

Back

To graph a linear function, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through the points.