Draw the graphs of the functions y=1.2x+.9 and y=−1.3x+4.4. using the graph, locate the points of intersection of the two graphs. now find the exact y and x coordinates of the point of intersection (use algebra).

To draw a graph of any linear function you need two points only.  We usually use x and y intercepts because these are easiest to work with. 
To find x-intercept we set y to be 0. This is also called zero of a function. Let us find x-intercepts for those two functions:


Now we simply set y=0 and solve for x:








Now we need to find y-intercepts. To do this we simply set x to be zero.





Graphs of our functions are not defined by these two points.


To draw a graph you simply draw a line through these two points.
To find intersection we can use a fact that at the point of intersection both functions have the same value. We can write that down mathematically this way:
-1.3x+4.4=1.2x+0.9
Now we need to solve for x. This will give us an x coordinate of the intersection point.


Now we simply plug in these value of x in any function to obtain y coordinate of the interception point.



Our intersection point the following coordinates (1.4,2.6).
I have attached the graph with all the points that we calculated highlighted.