Comparing Functions

Front

What is the slope of the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is.

Front

How do you identify the y-intercept in the equation y = mx + b?

Back

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

Front

What does a greater slope indicate about two linear equations?

Back

A greater slope indicates that the line rises more steeply. If comparing two lines, the one with the greater slope increases faster.

Front

If two equations have the same slope, what can be said about their graphs?

Back

If two equations have the same slope, their graphs are parallel and will never intersect.

Front

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

Back

To compare y-intercepts, look at the constant term (b) in the equations. The larger the b value, the higher the y-intercept.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if two lines intersect at a point?

Back

If two lines intersect, it means they have different slopes and will have one unique solution for their equations.

Front

How can you determine if two equations have the same slope?

Back

Two equations have the same slope if their coefficients of x (m) are equal when in the form y = mx + b.

Front

What is the significance of the y-intercept in real-world scenarios?

Back

The y-intercept can represent the starting value of a situation, such as initial cost or starting population.

Front

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

Back

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