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If the graph of the line $y = ax + b$ passes through the points $(4,5)$ and $(8,17)$, what is $a - b$?

 Jul 3, 2020
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\(y = ax + b \) is our general form for this line.

We know the points (4,5) and (8,17) MUST satisfy this equation as they are part of this line. So, we can substitute this into the equation.

 

1) \(y = ax + b \)

    \(5 = 4a + b\)

 

Also,

2) \(y = ax + b \)

   \(17 = 8a + b\)

 

We can now solve this system of equations!

We subtract equation 1 from equation 2.

      \(17 = 8a + b\)

(\(-\)\(5 = 4a + b\)

                             

     \(12 = 4a\), isolate a by dividing by 4 on both sides.

     \(a = 3\)

 

Now, we can find be by substituting the value of a into either equation.

   \(5 = 4a + b\)

\(​​​​5 = 4(3) + b\), subtract 12 from both sides.

   \(b = -7\)

 

However, this is not our answer! MAKE SURE TO ALWAYS ANSWER THE QUESTION!!

\(a - b = 3 - (-7) = 10\)

 

So, \(a - b = 10\)

Hope this helps Guest!

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 Jul 3, 2020

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