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the graph of a function is a line that passes through the coordinates (2,11) and (8,14) write an equation in the form y=mx +b for this function.

Respuesta :

ghanami

Answer:

Step-by-step explanation:

Hello : let  A(2,11)    B(8,14)

the slope is :  m = (YB - YA)/(XB -XA)

(14-11)/(8-2)  = 3/6 = 1/2

the slope is  m=1/2 so : y=1/2 x +b

passes through A(2,11)    B(8,14)

for exempl  A(2,11) ; when x=2    y =11

1/2(2)+b = 11

b = 10

an equation in the form y=mx +b for this function is :

y=1/2 x +10

shristiparmar1221

This question is based on the equation of line. Therefore,  an equation in the form y=mx +b for this function is [tex]y=\dfrac{1}{2} x +10[/tex].

Given:

The graph of a function is a line that passes through the coordinates (2,11) and (8,14).

We need to determined the equation in the form y=mx +b for this function.

According to the question,

Let  A  be (2,11) and B be (8,14).

Then slope is :

[tex]m = \dfrac{(Y_B - Y_A)}{(X_B -X_A)}[/tex]  

[tex]m = \dfrac{14 - 11}{8 - 2} \\\\m=\dfrac{3}{6}\\\\ m=\dfrac{1}{2}[/tex]

Then, equation will becomes,

[tex]y=\dfrac{1}{2} x +b,[/tex] passes through A(2,11) and B(8,14)

For example: Let us take A(2,11) ; where x=2 and y =11.

Putting this points in above equation of line.

We get,

⇒[tex]11= 2\dfrac{1}{2} +b[/tex]

⇒ b = 10

Therefore,  an equation in the form y=mx +b for this function is [tex]y=\dfrac{1}{2} x +10[/tex].

For more details, prefer this link:

https://brainly.com/question/25557784

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