Answer:
[tex]y=13x+32[/tex]
Company will produce 149 engines in 9th year.
Step-by-step explanation:
We have been given a graph that shows the number of engines produced each year since the company started operations. We are asked to write a function for the given dot plot.
We will use two points on the graph to find slope of the line passing through these points. We can see that point (2,60) and (5,99) is on our given graph.
[tex]m=\frac{99-60}{5-2}=\frac{39}{3}=13[/tex]
So the slope of the line is 13.
Now we will use point-slope form as:
[tex]y-60=13(x-2)[/tex]
[tex]y-60=13x-26[/tex]
[tex]y-60+60=13x-26+60[/tex]
[tex]y=13x+34[/tex]
Upon looking at our given choices, we can see that function [tex]y=13x+32[/tex] is the correct choice.
Now we will substitute [tex]x=9[/tex] to find the engines produced by company in 9th year as:
[tex]y=13(9)+32[/tex]
[tex]y=117+32=149[/tex]
Therefore, company will produce 149 engines in 9th year.
