Lines in Context

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 line represent?

Back

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

Front

What is the y-intercept of a graph?

Back

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

Front

How do you find the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is the formula for a linear equation in slope-intercept form?

Back

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

Front

What does the term 'rate of change' refer to?

Back

The rate of change refers to how much one quantity changes in relation to another quantity, often represented by the slope in a linear function.

Front

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

Back

In real-world scenarios, the y-intercept often represents the starting value or initial condition of a situation at the point where the independent variable is zero.

Front

How can you identify the y-intercept from a graph?

Back

You can identify the y-intercept from a graph by locating the point where the line crosses the y-axis.