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).
Accepted Solution
A:
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.