Linear Functions - 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 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

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x = 0 and solve for y. The value of y at this point is the y-intercept.

Front

What is the y-intercept of the equation y = 3x - 5?

Back

The y-intercept is -5.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x. The value of x at this point is the x-intercept.

Front

What are the x- and y-intercepts of the equation 2x - y = 6?

Back

The x-intercept is (3, 0) and the y-intercept is (0, -6).

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases. This is indicated by a positive slope.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, y decreases. This is indicated by a negative slope.

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.

Front

How do you graph a linear function?

Back

To graph a linear function, identify the y-intercept, plot it on the graph, use the slope to find another point, and draw a straight line through the points.