The points (-2, -4), (0,0), (4,a) and (b, 18) is on a straight line . What is the number a and b?

I wonder if it is possible to calculate the answer to the question, or are you just simply doing guesswork? 
I don't know if I'm solving it the right way.

The answer is a = 8 and b = 9

Guest Oct 22, 2014

Best Answer 


Thanks guys so much for the answers! People like you are gold when you're trying to learning math without a teacher!

Guest Oct 22, 2014

No..we don't usually like to do too much "guessing" on here....

Since all the points lie on a line, the slope between them will be the same. So the slope between (-2, -4) and (0, 0) = [-4 - 0]/ [-2, 0] = -4/-2 = 2

So, using this, the slope between (0, 0) and (4, a) = 2  ....and we have..

[a - 0] / [4 - 0] = 2   → a/4 = 2  → (multiply both sides by 2)......a = 8.


[18 - 0 ] / [ b - 0] =  2  →  18/2 = b → 9 = b


And that's it .....(without the guesswork .....!!!)


CPhill  Oct 22, 2014

Points (-2, -4), (0,0), (4,a) and (b, 18)

If they're all on the same line, then they're all on the same slope, or share the same "m" value in y=mx+b. Now, in the first two ordered pairs, the x values are -2 and 0. The y values are -4 and 0. For each respective ordered pair, the equations can be made:



If you take the second equation, you can solve for b easily, because anything times 0 is 0.




So, since this is all on the same line, or slope, that value of b works in the other equation.


Now, solve for m! You can drop the plus 0, and then divide by -2 on both sides.




So, now we know m=2 and b=0. We can plug these into our slope-intercept equation. From now on:


Or, simply,


Now, we need to solve for (4,a) and (b, 18).

In the first one, we know the x value, 4, but need to find y, which is a.



In the second one, we know the y value, 18, but need to find x, which is b.



So you were right! a=8 and b=9.

SIDE NOTE: Because one ordered pair was (0,0), we could skip a step to find b in y=mx+b. Normally, this is how it would be done:

Find slope-intercept form of (-2,-4) and (0,0)



Rewrite both equations so b is left alone. On the first one, subtract m(-2) from both sides.


This could be rewritten as -(-2m), or simply +2m.


Now, subtract m(0) from both sides of the second equation


So, if -4+2m=b, and b=0-m0, we can squish that all together:



Then, you would go about solving for m like you would in any equation by moving all the b values to one side and all the constants (numbers without variables) to the other. We will add 0 to both sides, and subtract -2m from both sides. This will put the constants on the left and the m values on the right.



Now, dividing -4/-2 gets:


Just like it did before! Now you plug this back into the equations (the ones using points (-2,-4) and (0,0) in the slope-intercept equation y=mx+b) to get your b value. Then solve the rest like you did already!

Guest Oct 22, 2014
Best Answer

Thanks guys so much for the answers! People like you are gold when you're trying to learning math without a teacher!

Guest Oct 22, 2014

Hi anon asker,

Gracious people like you make our efforts all worthwhile.  :)

Thank you :)))


To Chris and anon answerer;

Great answers there.  Thanks 

Melody  Oct 22, 2014

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