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What is the equation of the line that passes through the points (-1, 3) and (1, 11)?

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1 Answer

We're going to use the point-slope equation and apply it twice.  First, we'll use it with both points to get a slope.  Then we'll use the slope with just one point to get an equation.
 
The form of the point slope form is this: y - y1 = m(x-x1)
 
(x, y) is the first point: we'll use (1, 11)
(x1, y1) is the second point: we'll use (-1, 3)
m is the slope, currently unknown
 
First, we'll plug in the two points and solve for m.
 
11 - 3 = m(1 - [-1]) [plugged in (1,11) for (x, y) and (-1, 3) for (x1, y1)]
11 - 3 = m(1 + 1) [subtracting a negative is identical to adding a positive]
8 = 2m [did addition/subtraction on both sides]
m = 8/2 [divided both sides by 2]
m = 4 [simplified]
 
So our slope m is equal to 4.  Now we'll take that slope and one of the two points and put it back into the point-slope equation.  Note that we'll put it in for the point (x1, y1).  We could also put it in for (x, y) and get the same answer, but this usually works out more easily.  We'll use the point (1, 11) so we don't have to deal with negatives, also making things simpler.  Using (-1, 3) would have been equally valid.
 
y - 11 = 4(x - 1) [plugged in values for our point (x1, y1) and our slope m]
y - 11 = 4x - 4 [distributed the 4 over the quantity (x - 1)]
y = 4x + 7 [added 11 to both sides]
 
Answer: y = 4x + 7
 
Now this is a valid answer, but it's not one of the ones given.  This is fine, we just need to rearrange things to get the form your question is looking for.  It seems to want x and y on the same side of the equation, so let's do that.
 
y = 4x + 7
4x + 7 = y [flipped the two sides]
4x - y + 7 = 0 [subtracted y from both sides]
4x - y = -7 [subtracted 7 from both sides]
 
Final Answer: 4x - y = -7

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