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# linear functions

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The points (5,r) and (3,-2) lie on a line with a slope of -2.  What is the value of r?

Mar 29, 2021

#1
+101
+2

To calculate the slope, we need the Delta Y over the Delta X.

So, the delta Y is: -2 - r

And the Delta X is: 3 - 5

We are left with:

$$\begin{array}{l}\frac{-2-r}{3-5}\ =\ -2\\ \\ =\ \frac{-2-r}{-2}=-2\\ =-2-r\ =\ 4\\ -r\ =\ 4\ +2\\ r\ =\ -6\\ \\ \\ \end{array}$$

Therefore the value of r = -6.

Heres the proof

(5, -6) --> (3, -2)

m = -2 - (-6)  ÷  (3 - 5)

= 4 / -2 = -2.

Therefore r = -2

(Solved by a 12 y/o - Yep! )

Mar 29, 2021

#1
+101
+2

To calculate the slope, we need the Delta Y over the Delta X.

So, the delta Y is: -2 - r

And the Delta X is: 3 - 5

We are left with:

$$\begin{array}{l}\frac{-2-r}{3-5}\ =\ -2\\ \\ =\ \frac{-2-r}{-2}=-2\\ =-2-r\ =\ 4\\ -r\ =\ 4\ +2\\ r\ =\ -6\\ \\ \\ \end{array}$$

Therefore the value of r = -6.

Heres the proof

(5, -6) --> (3, -2)

m = -2 - (-6)  ÷  (3 - 5)

= 4 / -2 = -2.

Therefore r = -2

(Solved by a 12 y/o - Yep! )

MathyGoo13 Mar 29, 2021
#2
+117787
0

Good job, MG!!!!!

CPhill  Mar 29, 2021
#3
+101
+1

Thanks!

MathyGoo13  Mar 29, 2021