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 (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Front

What is the y-intercept (b) in a linear equation?

Back

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

Front

How do you write the equation of a linear relationship from a word problem?

Back

Identify the initial value (y-intercept) and the rate of change (slope) from the problem, then use the format y = mx + b to write the equation.

Front

If a savings account starts with $500 and loses $20 per month, what is the equation for the savings after m months?

Back

s = -20m + 500.

Front

What is the unit rate in a linear relationship?

Back

The unit rate is the slope of the line, representing how much one variable changes for a one-unit change in another variable.

Front

In the equation y = 3x + 5, what is the slope and y-intercept?

Back

The slope is 3 and the y-intercept is 5.

Front

How can you determine if a relationship is linear from a table of values?

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, the relationship is linear.

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).