Functions, Linear vs NonLinear, Write Equations

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Tags

CCSS.8.F.A.1

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions create straight lines when graphed, while nonlinear functions create curves.

Tags

CCSS.8.F.A.3

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are constants.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).

Front

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

Back

Use the point-slope form: y - y1 = m(x - x1).

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed, such as quadratic or exponential functions.

Tags

CCSS.8.F.A.3

Front

What is the equation of a line that passes through the points (3, 4) and (0, -5)?

Back

y = 3x - 5.