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A line through the points (2, -9) and (j, -17) is parallel to the line 2x + 3y = 21. What is the value of j?

 Jun 5, 2021
 #1
avatar+32758 
+2

2x + 3y = 21 

is the same as    y = -2/3x + 7    slope , m = -2/3

 

Parallel slope is the same slope   -2/3

 

(-9- -17) / (2-j) = - 2/3     solve for 'j'

 Jun 5, 2021
 #2
avatar+1893 
+1

2x + 3y = 21

3y = -2x + 21

y = -2/3x + 7

So the slope of that line is -2/3, meaning this line has to have the same slope. 

y = -2/3x + b

Plugging in (2, -9)

2 = -2/3(9) + b

2 = -6 + b

b = 8

So our equation is y = -2/3x + 8

We're solving for j. 

-17 = -2/3j + 8

-25 = -2/3j

j = 37.5

 

=^._.^=

 Jun 5, 2021
 #3
avatar+1893 
0

Edit:

I switched the x and the y on (2, -9)

-9 = -2/3(2) + b

-27/3 = -4/3 + b

b = -23/3

 

y = -2/3x - 23/3

-17 = -2/3(j) - 23/3

oops

 

=^._.^=

catmg  Jun 5, 2021

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