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:
[tex]y=1.2x+0.9[/tex]
[tex]y=-1.3x+4.4[/tex]
Now we simply set y=0 and solve for x:
[tex]0=1.2x+0.9[/tex]
[tex]0=-1.3x+4.4[/tex]

[tex]1.2x=-0.9[/tex]
[tex]1.3x=4.4[/tex]

[tex]x=-0.75[/tex]
[tex]x=3.4[/tex]
Now we need to find y-intercepts. To do this we simply set x to be zero.
[tex]y=1.2x+0.9[/tex]
[tex]y=-1.3x+4.4[/tex]

[tex]y=0.9[/tex]
[tex]y=4.4[/tex]
Graphs of our functions are not defined by these two points.
[tex]y=1.2x+0.9; (0,-0.75),(0.9,0)[/tex]
[tex]y=-1.3x+4.4; (0,3.4),(4.4,0)[/tex]
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.
[tex]2.5x=3.5[/tex]
[tex]x=1.4[/tex]
Now we simply plug in these value of x in any function to obtain y coordinate of the interception point.
[tex]y=1.2x+0.9[/tex]
[tex]y=1.2(1.4)+0.9[/tex]
[tex]y=2.6[/tex]
Our intersection point the following coordinates (1.4,2.6).
I have attached the graph with all the points that we calculated highlighted.