SOLUTION: the question is: The given ordered pairs are solutions of the same linear equation. Find N. (0,1), (4,9), (3,N) The book gives the answer as 7. Fine, but how the heck did

Question 73752This question is from textbook beginning algebra
: the question is:
The given ordered pairs are solutions of the same linear equation. Find N.
(0,1), (4,9), (3,N)
The book gives the answer as 7. Fine, but how the heck did they get the answer. I can't find anything in the chapter which gives me a hint about how to solve this question. Help !! This question is from textbook beginning algebra

Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since this is a linear equation (it is a line) the points (0,1), (4,9), (3,N) will all be on the same line. So lets find the equation for the line through the points (0,1), (4,9). First we need the slope

Solved by pluggable solver: Finding the Equation of a Line

First lets find the slope through the points (,) and (,)

Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope is

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Now let's use the point-slope formula to find the equation of the line:

------Point-Slope Formula------
where is the slope, and (,) is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get

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Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

Notice how the two points lie on the line. This graphically verifies our answer.

Now use the slope and the point (0,1) to find the equation.
Plug in m=2 and (0,1)

So any more solutions will lie on this line. So to find N, just plug in x=3 to find y

So the solution is (3,7) which supports the answer. Hope this makes sense. Draw the graph and the points if this is hard to understand.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The three given points all lie on the same line, right? Why?, because, you are told, they all are solutions to the same linear equation.
So, we can start by finding the slope of the line, using the first two of the three points.
Substitute (0,1) and (4,9).

This is the slope of the line. The third point also lies on this line so we can use it, along with one of the other two points, in the slope formula, remembering that m = 2.

Multiply both sides by -1.
Add 9 to both sides.
or
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