Question 1159296
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Answer: <font color=red size=4>y = x + 1</font>
slope = 1, y intercept = 1
You can think of y = x+1 as y = 1x + 1


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Work Shown:


Find the slope of the line through (x1,y1) = (-2,-1) and (x2,y2) = (2,3)
m = (y2 - y1)/(x2 - x1)
m = (3 - (-1))/(2 - (-2))
m = (3 + 1)/(2 + 2)
m = 4/4
m = 1


Plug m = 1 and (x1,y1) = (-2,-1) into the point slope formula. Solve for y.
y - y1 = m(x - x1)
y - (-1) = 1(x - (-2)) ... substitution
y + 1 = 1(x + 2) ... subtracting a negative is the same as adding
y + 1 = x + 2
y + 1 - 1 = x + 2 - 1 ... subtract 1 from both sides to isolate y
y = x + 1


To confirm we have the correct answer, lets test out the point (-2, -1). This means x = -2 and y = -1 pair up together
y = x+1
-1 = -2+1 ... replace x with -2, y with -1
-1 = -1 ... true equation
since we get a true equation (ie the same number on both sides), this means we have confirmed (-2,-1) as a solution. Let's check the other ordered pair.


Plug in (x,y) = (2,3)
y = x+1
3 = 2+1 ... replace x with 2, y with 3
3 = 3 ... also true
We have confirmed both points, so this fully confirms the answer.


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If you wish to have the equation in standard form (Ax+By = C), then one way is to do the following steps
y = x + 1
y-x = x+1-x ... subtract x from both sides
-x+y = 1
-x+y = 1 .... technically this is in standard form, but many books require that A > 0
-1(-x+y) = -1*1 ... to make A > 0, multiply both sides by -1
x-y = -1 ... distribute and multiply


x-y = -1 is in the form Ax+By = C where A = 1, B = -1, C = -1
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