Linear Graphing

Front

What is 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 slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.

Front

How can you identify a linear function from a set of points?

Back

A function is linear if the points lie on a straight line when graphed. The differences in y-values divided by the differences in x-values (rise over run) should be constant.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the slope-intercept form y = mx + b.

Front

What does a vertical line represent in a graph?

Back

A vertical line represents an equation of the form x = a, where 'a' is a constant. It indicates that for every value of y, x remains constant.

Front

What does a horizontal line represent in a graph?

Back

A horizontal line represents an equation of the form y = b, where 'b' is a constant. It indicates that for every value of x, y remains constant.

Front

What is 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, a circle, or any other shape that is not linear.

Front

How can you tell if an equation is nonlinear?

Back

An equation is nonlinear if it contains variables raised to a power other than one, products of variables, or functions like sine, cosine, etc.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change in real-world contexts, such as speed, cost per item, or growth rates.