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Find the slope and the y-intercept for the line that passes through (-7,-12) (3,12)

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2 Answers

Given the two points on the line (-7, -12) and (3, 12). We can find both the slope and the y-int using the equation of a line
 
y = mx + b
 
Step 1:
Find the Slope
 
m = (y- y1) / (x2 - x1) - pick your points (I will say (3, 12) is point 1 and (-7,-12) is point 2) 
= ((-12) - 12) / ((-7) - 3) = -24/-10 
which can be reduced to 12/5
 
Step 2:
Find y-int
 
(Using the equation of the line y = mx +b)
  1. pick a point (I picked (3,12) )
  2. plug in x,y, and m value
 
we get... 12 = (12/5)*(3) + b
 
Lets solve for b
 
12 - (36/5) = b    (subtract (12/5)*3 from both sides to get b alone)
 
60/5 - 36/5 = b   (convert to common denominator by multiplying by 5)
 
24/5 = b
 
Now we have the equation of the line
y =     m  x  +    b
y = (12/5)x + (24/5)
 
 
We know two points on the line: (-7, -12) and (3, 12)
 
slope = (y2 - y1)/(x2 - x1) = [12 - (-12)]/[3 - (-7)] = (24/10) = (12/5)
 
So we now know that the equation of the line is
 
y = (12x/5) + b, where be is the y-intercept
 
Substituting the values of x and y for one of the points (3, 12) gives
 
12 = [(12)(3)/(5)] + b
 
b = 12 - [(12)(3)/(5)] = 12 - (36/5) = [(60 - 36)/5) = (24/5)
 
y = (12x/5) + (24/5)
 
Double check:
 
Does -12 = [(12)(-7)/5] + (24/5)?
 
Does -12 = (-84/5) + (24/5)?
 
Does -12 = (-60/5)
 
YES!!!