Understanding Linear Functions and Graphs

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 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

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

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x to 0 and solve for y. The value of y when x = 0 is the y-intercept.

Front

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

Back

The formula for calculating slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a linear function?

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 about a linear function?

Back

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

Front

What is a scatter plot?

Back

A scatter plot is a graph that shows the relationship between two quantitative variables. Each point represents an observation.

Front

What does it mean if a scatter plot shows a positive correlation?

Back

A positive correlation in a scatter plot means that as one variable increases, the other variable also tends to increase.

Front

What does it mean if a scatter plot shows a negative correlation?

Back

A negative correlation in a scatter plot means that as one variable increases, the other variable tends to decrease.

Front

What is the y-intercept in the equation y = 1/2x - 1?

Back

The y-intercept in the equation y = 1/2x - 1 is -1.