Linear Functions

Front

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

Back

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

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

How do you determine if a graph represents a function?

Back

A graph represents a function if it passes the vertical line test, meaning no vertical line intersects the graph at more than one point.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you write an equation from a word problem involving linear relationships?

Back

Identify the variables, determine the relationship between them, and express it in the form of a linear equation.

Front

What is the meaning of the slope in a linear function?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How do you find the y-intercept from a linear equation in slope-intercept form?

Back

In the equation y = mx + b, the y-intercept is the value of b.

Front

What is a real-world example of a linear function?

Back

A real-world example is the relationship between distance and time at a constant speed, represented by the equation d = rt.

Front

What is the significance of the rate of change in a linear function?

Back

The rate of change indicates how much the dependent variable changes for a unit change in the independent variable.