Linear/Nonlinear/Equations from tables

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed. It has a constant rate of change.

Front

What is a nonlinear equation?

Back

An equation that does not form a straight line when graphed. The rate of change is not constant.

Front

How do you determine if a relationship is linear or nonlinear from a table of values?

Back

If the rate of change between values is constant, the relationship is linear. If it varies, it is nonlinear.

Front

What is the rate of change in a linear function?

Back

The rate at which the dependent variable changes with respect to the independent variable, often represented as 'slope'.

Front

What does a slope of -2 indicate?

Back

For every 1 unit increase in the x-value, the y-value decreases by 2 units.

Front

How can you find the slope from a table of values?

Back

Choose two points (x1, y1) and (x2, y2) and use the formula: slope = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the points (1, 3) and (3, 7)?

Back

The slope is 2.

Front

What does it mean if a function has a constant slope?

Back

It means the function is linear.

Front

What is an example of a nonlinear function?

Back

y = x^2 is a nonlinear function because it forms a curve when graphed.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, representing the value of y when x = 0.