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Answer:
Step-by-step explanation:
We are given that the graph of the equation:
Passes through the three points (0, 5), (1, 10), and (2, 19).
And we want to find the value of (<em>a</em> + <em>b</em> + <em>c</em>).
First, since the graph passes through (0, 5), its <em>y-</em>intercept or <em>c</em> is 5. Hence:
Next, since the graph passes through (1, 10), when <em>x</em> = 1, <em>y</em> = 10. Substitute:
Simplify:
The point (2, 19) tells us that when <em>x</em> = 2, <em>y</em> = 19. Substitute:
Simplify:
This yields a system of equations:
Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:
Add the two equations together:
Combine like terms:
Hence:
Using the first equation:
Therefore, our equation is:
Thus, the value of (<em>a</em> + <em>b</em> + <em>c</em>) will be: