A linear function is an expression that gives you a straight line. The name is slightly revealing. Here, you will learn how to draw and recognize linear functions.
A linear function can be written on the form
where is the slope, and is the intersection with the -axis.
You can find the slope of a line if you have the coordinates of two points on the line. Call the points and . You use the following formulas for the slope and the constant term :
The straight line that goes through the points and has the slope
and the constant term
The slope tells you how much the graph is increasing/decreasing when increases by 1.
If , the graph rises towards the right, and if , the graph is sinking towards the right.
The graph intersects the -axis in the point .
The graph is a straight line with coordinates .
Find the slope of the straight line that goes through the points and , and find where it intersects with the -axis
You choose to be and . The calculations would work even if you switched the points. You get
You now know that the line decreases by 2 when you move one place to the right. Let’s see what the point of intersection with the -axis is:
Thus, the point of intersection with the -axis is .