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Find the equation of a line through the points (-2,1) and (3,6)

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2 Answers

Hi John;
(-2,1) and (3,6)
First, let's establish slope.
Slope is the change-of-y divided by the change-of-x.
slope=(y-y1)/(x-x1)
slope=(1-6)/(-2-3)
slope=-5/-5
slope=1
Let's take one point and use the point-slope formula.  I randomly select the first point, (-2,1)
y-y1=m(x-x1)
y-1=1(x--2)
Subtracting a negative number is the same as adding a positive number...
y-1=x+2
Let's add 1 to both sides...
1+y-1=x+2-1
y=x+3
Let's apply the other point,  (3,6), to verify...
6=3+3
6=6
First of all, you find the slope of the line, by finding, (the distance in y)/(the distance in x)= (6-1)/(3-(-2))=? (I think you should do that yourself, this is easy).
 
After you find the slope, say its a value, called a. You will insert a, into the slope-intercept form of the linear equation: y=ax+b. You could use either (-2, 1) as your (x, y), or (3, 6), as your (x, y). Now you know a, x, y, solve for b. This shouldn't be too hard either. I think you should do it yourself.