#linear functions

Functions_9th Grade.Math course..pdf

● Graphing linear functions means drawing straight lines on a coordinate plane using linear equations like y = mx + b. ● Find two points by plugging in x values to solve for y, then plot these points and draw a line through them

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Last time I went over the general concept of graphing; here I will go over the graph of a line. The general equation of a line is y=mx+b, where m is the slope of the line and b is the y-intercept of the line. The slope is how much the y variable changes for a corresponding change in x. For example, if the slope is 2, then the y variable increases by two units for every one unit increase in the x…

The formula of the graph already is the formula to give you all points that lie on the graph (because it’s basically made of an infinite number of points that form a line).

You can stick pretty much any number in as x (this would be the x-coordinate of the point) and then you can calculate y (this would be y-coordinate of the point). Those two coordinates are enough to define a point here.

You should not try x=3 though, because x-3=3-3=0 and dividing by 0 is Bad News.

Pretty much any other number should be good though, for example:

x=5 [randomly chosen by the power of my mind]

y= 1/(x-3) = 1/(5-3) = ½

Point A (5/0.5) [you can write ½ instead of 0.5, I just didn’t want the slashes to get confusing]

Any pair of numbers (x/y) for which the equation y= 1/(x-3) is true, gives you the coordinates of a point that lies on the relating graph.

I hope you can come up with a second point now.