Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of 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 in a linear relationship?

Back

The slope of a line represents the rate of change between the two variables. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you calculate the rate of change from two points on a graph?

Back

The rate of change can be calculated using the formula: (change in y) / (change in x) = (y2 - y1) / (x2 - x1).

Front

What is the equation of a line in slope-intercept form?

Back

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

Front

If a line has a slope of 8, what does this mean in terms of rate of change?

Back

A slope of 8 means that for every 1 unit increase in x, y increases by 8 units.

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a function divided by the change in the input value over a specific interval.

Front

How can you represent a linear relationship using a table?

Back

A linear relationship can be represented in a table by listing pairs of x and y values that satisfy the linear equation.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) represents the y-intercept of the line, where the line crosses the y-axis.