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the line Ay = Bx + 1 goes through the points (1, 3) and (5, 13).

 May 19, 2018
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Hey bigguy1989!

 

To solve for A and B, we plug in our two values for x and y to set up the systems of equations. 

 

When x = 1 and y = 3: (1,3), we get: 3A = B + 1

When x = 5 and y = 13: (5,13), we get: 13A = 5B + 1

 

 

We obtain the systems: 

 

3A = B + 1

13A = 5B + 1

 

To solve the systems, we multiply the top one by 5, and we get:

 

3A = B + 1 \(\Rightarrow\) 15A = 5B + 5

 

Now we can subtract first equation from second equation so the B's cancel out. 

 

15A - 13A = 5B - 5B + 5 - 1

 

2A = 4

A = 2 \(\Rightarrow\) B = 5

 

The line becomes 2y = 5x + 1

 

In standard form: 2y - 5x = 1

 

In slope-intercept: y = 2.5x + 0.5

 

I hope this helped,

 

Gavin

 May 19, 2018

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