SOLUTION: I'm trying to figure out this problem to help my son with his homework. Write the equation of a line that passes through (-2,-1) and (2,3).

Question 1159296: I'm trying to figure out this problem to help my son with his homework.
Write the equation of a line that passes through (-2,-1) and (2,3).

Found 3 solutions by ikleyn, josgarithmetic, jim_thompson5910:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

It is very elementary and basic skill that every student must develop to the level to solve such problems on his (or her)
own without asking assistance from outside.

To help you to develop such skills, the special lesson was created in this site
    - Equation for a straight line in a coordinate plane passing through two given points

Read it and then solve your problem.

From this lesson, learn the subject once for all.

At the end of this lesson, you will find the links to other lessons, covering the entire, more wide, subject.
Do not miss these lessons.

Consider them as your textbook, handbook, tutorials and (free of charge) home teacher.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Slope is .

m is for "slope".

Substitute either of the given points to be on the line:

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Answer: y = x + 1
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.

------------------------

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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