contestada

What is the rate of change and initial value for the linear relation that includes the points shown in the table

X Y
2 3
4 5
6 7
8 9

Respuesta :

[tex]\bf \begin{array}{ccllll} x&y\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 2&3\\ \boxed{4}&\boxed{5}\\ 6&7\\ \boxed{8}&\boxed{9} \end{array}\impliedby \textit{we could use any \underline{two pairs}}\\\\ -------------------------------\\\\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 4}}\quad ,&{{ 5}})\quad % (c,d) &({{ 8}}\quad ,&{{ 9}}) \end{array}[/tex]

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{9-5}{8-4}\implies \cfrac{4}{4}\implies 1 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-\boxed{5}=1(x-\boxed{4})\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-5=x-4\implies y=x-4+5\implies \begin{array}{llll} y=&1x&+1\\ &\uparrow &\ \uparrow \\ &slope&y-intercept\\ &&\textit{initial value} \end{array}[/tex]
boffeemadrid

The rate of change of the given values is required.

The rate of change of the given relation is 1.

The initial value is [tex](0,1)[/tex]

The values are

[tex](2,3)[/tex]

[tex](4,5)[/tex]

[tex](6,7)[/tex]

[tex](8,9)[/tex]

The rate of change or slope is given by

[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

[tex]\Rightarrow m=\dfrac{5-3}{4-2}[/tex]

[tex]\Rightarrow m=\dfrac{2}{2}[/tex]

[tex]\Rightarrow m=1[/tex]

The rate of change of the given relation is 1.

The equation of the line will be

[tex]y-3=1(x-2)\\\Rightarrow y=x+1[/tex]

The initial value

[tex]x=0[/tex]

[tex]y=0+1=1[/tex]

[tex](0,1)[/tex]

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