SOLUTION: Find an equation of the line containing the given pair of points. (-3, -2) and (-7, -1) The equation of line y is? Help please.

Question 136435: Find an equation of the line containing the given pair of points.
(-3, -2) and (-7, -1)
The equation of line y is?
Help please.
Found 2 solutions by Earlsdon, algebrapro18:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You can start with the slope-intercept form of a linear equation:
where m is the slope and b is the y-intercept.
Let's find the slope, m, using the slope formula:
The x's and y's are taken from the two given points: (-3, -2) = (,) and (-7, -1) = (,) So, making the appropriate substitution, we get:
Simplifying,...

So you can start your equation with:
Now you need to find the value of b, the y-intercept.
You can do this by substituting the x- and y-coordinate from either of the two given points into the equation above and solving for b. Let's use the first point (-3, -2) for the x and y.
Simplify.
Subtract from both sides.

Now you can write the final equation:

Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
First you need to fine the slope of this line. You do this using the formula for slope which is:

m = (y2-y1)/(x2-x1)where
x1 = -3
y1 = -2
x2 = -7
y2 = -1

now plugging in you get

m = (-1-(-2))/(-7-(-3))
m = (-1+2)/(-7+3)
m = 1/-4
m = -1/4

now that we know the slope we can find the equation of the line in two ways.

Method 1: solving y=mx+b for b

Now that we have numbers for y,m, and x we can plug those into the slope-intercept formula and solve for b.

y = mx + b
-1 = -1/4(-7) + b
-1 = 7/4 + b
-11/4 = b

y = -1/4x - 11/4

Method 2: use the point slope formula and solve for y

There is another formula you may not have used yet, its call the point slope formula. It looks like this:

y-y1=m(x-x1)where
x1 = -3
y1 = -2

now plugging in you get

y-(-2)=-1/4(x-(-3))
y+2 = -1/4(x+3)
y = -1/4x - 3/4 -2
y = -1/4x - 11/4

Either method you use will give you the same line so really its personal preference(or what ever way your teacher specifies).
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