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Based on the table of values below, find the slope between points where x = 1 and where x = 4.

X: 1 , 3 , 4
Y: 8, 6, -1

Answer Choices:
A. −3
B. Negative two thirds
C. Three over two
D. 3

Respuesta :

[tex]\bf \begin{array}{llll} x&\boxed{1}&3&\boxed{4}\\\\ y&\boxed{8}&6&\boxed{-1} \end{array}\\\\ -------------------------------\\\\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 8}})\quad % (c,d) &({{ 4}}\quad ,&{{ -1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-1-8}{4-1}\implies \cfrac{-9}{3}\implies -3[/tex]

Answer:

The slope between the points where x=1 and where x=4 is :

-3

i.e. option: A is the correct answer.

Step-by-step explanation:

Let Y=f(X)

We are given a table of values as:

X: 1 , 3 , 4

Y: 8, 6, -1

Let m represents the slope .

We know that the slope between the points x=a and x=b is give by:

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

Here we are asked to find the slope between x=1 and x=4

i.e. we have:

a=1     and   b=4

f(a)=8   and    f(b)= -1

Hence, the slope between x=1 and x=4 is calculated as:

[tex]m=\dfrac{-1-8}{4-1}\\\\m=\dfrac{-9}{3}\\\\m=-3[/tex]

Hence, the slope is:

-3

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