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Y_Kistochka [10]
3 years ago
14

Write an equation of a line that passes through the points (1, 7) and (5, 19) . Give the final form in slope intercept form. (Pl

ease no fake answers or Links)
Mathematics
1 answer:
Alinara [238K]3 years ago
3 0

Answer:

y = 3x + 4

Step-by-step explanation:

slope = (y2 -y1)/(x2 - x1)

y2 = 19

y1 = 7

x2 = 5

x1 = 1

Slope = (19 - 7)/(5 - 1)

slope = 12 / 4

slope = 3

So far what you have is

y = 3x + b                      To solve for b, use either of the two points.

x = 1

y = 7

7 = 3(1) + b

7 = 3 + b

b = 4

The final equation is

y = 3x + 4                    

We should check that with the other  point

x = 5                  Find y

y = 3(5) + 4

y = 15 + 4

y = 19              Ans it checks.

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\green{\large\underline{\sf{Solution-}}}

<u>Given expression is </u>

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\purple{\rm :\longmapsto\:\boxed{\tt{ \:  \:   {x}^{m} \times  {x}^{n} =  {x}^{m + n} \: }}} \\

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\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 4}  -  {5}^{2n + 2} }

can be further rewritten as

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 2 + 2}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2}  - 1)}

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<u>Hence, </u>

\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }  =  \frac{1}{6} }}

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