7.7a/7.4a 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 the equation 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 between the two variables. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept?

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 y-intercept from an equation?

Back

To find the y-intercept from an equation in the form y = mx + b, identify the value of b.

Front

What is the constant rate of change?

Back

The constant rate of change is the same as the slope of the line. It indicates how much one variable changes in relation to another.

Front

What does it mean if a line has a negative slope?

Back

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

Front

What does it mean if a line has a positive slope?

Back

A positive slope means that as one variable increases, the other variable also increases.

Front

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

Back

A relationship is linear if the differences between the y-values divided by the differences between the x-values are constant.

Front

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

Back

The formula for finding the slope (m) is m = (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.