8.F.3, 8.F.4, and 8.F.5

Front

What is the definition of 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 is the definition of a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its graph can be a curve or any other shape that is not a straight line.

Front

How do you determine if a function is linear or nonlinear?

Back

To determine if a function is linear, check if it can be expressed in the form y = mx + b. If it cannot, or if its graph is not a straight line, it is nonlinear.

Front

What does the slope (m) represent in the slope-intercept form of a linear equation?

Back

The slope (m) represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What does the y-intercept (b) represent in the slope-intercept form of a linear equation?

Back

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

Front

If m = 3 and b = 6, what is the slope-intercept equation?

Back

The slope-intercept equation is y = 3x + 6.

Front

What is the slope of the line represented by the equation y = 4x + 12?

Back

The slope of the line is 4.

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.