How do you determine the value of 4 so that (5,r), (2,3) has slope 2?

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Answer 1 · 2017-11-19T12:08:20

It all depends on the formula slope #= (y_2-y_1)/(x_2-x_1)#

Here,

#"slope" = 2#

Using the formula, we get

#2 = (3-r)/(2-5)#

So ,

#3-r = -6#

#-r = -9#

Hence, the value of #r# is #9#.

Answer 2 · 2017-11-19T12:09:03

r = 9

The formula for slope is
m = #(y - y_1)/(x - x_1)#

You have one unknown, r, the value of one of the y's, so write in the given values of everything else and solve for r.

Let #(5,r)# be assigned as #(x,y)#
Let (2,3) be assigned as #(x_1,y_1)#

m = #(y - y_1)/(x - x_1)#

2 = #(r - 3)/(5 - 2)#
Solve for #r#

1) Combine like terms
2 = #(r - 3)/(3)#

2) Clear the fraction by multiplying both sides by 3 and letting the denominator cancel
#6 = r - 3#

3) Add 3 to both sides to isolate #r#
#9 = r# <-- answer

Answer
#r = 9#
...........................

Check
Sub 9 back into the original equation in the place of #r# and see if #m# will still equal #2#

#2 = (r−3)/(5−2)#

1) Sub in 9 in the place of #r#
#2# should still equal #(9−3)/(5−2)#

2) Combine like terms
#2# should still equal #(6)/(3)#

3) #2# does equal #2#
Check!