Question

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).

Answer 1

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:
$y=1.2x+0.9$
$y=-1.3x+4.4$
Now we simply set y=0 and solve for x:
$0=1.2x+0.9$
$0=-1.3x+4.4$

$1.2x=-0.9$
$1.3x=4.4$

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

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