What is y mx + c

Linear function

Linear function

Functional term, slope, y-axis intercept, zero point, functional rule

Function term - definition of function, definition range (definition set), value range (target range)

The definition range (also called definition set) is the set of numbers to which we assign a certain number from the range of values ​​(also: target range). We call this assignment a function. It is a clear rule.

Linear Function - From Proportional Function to Linear Function

Perhaps we still remember the proportional assignment. A proportional function is a straight line through the origin of the coordinates. We have a function rule for them y = m · x, where m is the proportionality factor. We will see later that this m is responsible for the slope of the straight line.

Draw linear functions - calculate points, draw and influence of the slope

We have our functional rule available, which is of the form y = mx + b. The slope m and the y-axis intercept b are specified therein. So we are given the task: Draw the linear function y = 2x - 3.

Determine the slope of a linear function - slope triangle and two-point form

We now want to determine the slope of a linear function. First we will see how we can read out its slope from a drawn graph and later any two points on this graph are sufficient. A very important term that one hears in connection with linear functions and their slope is the slope triangle. With the help of this gradient triangle we start. We have given an arbitrary linear function, the slope of which we do not yet know.

y-intercept - the intersection of the y-axis with the graph

For linear functions, the y-axis intercept is the value at which the function graph intersects the y-axis.

Zero of a linear function - set function to zero, calculate x

The zero point is the point on the x-axis at which the function graph intersects the x-axis. Since the point lies directly on the x-axis and the x-axis intersects the y-axis in the origin of the coordinates, the associated y-value is equal to zero, i.e. y = 0.

Create / construct functional rule for two given points

As a prerequisite, we have any two points. But we take two specific ones and calculate by way of example. We want a linear function through the points P (1 | 2) and Q (4 | 1). We don't know much, except that these two points lie on our line and that the function rule is of the form y = mx + b.