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3 years ago

Please help me because I don't understand how to do it.:)

Mathematics

1 answer:

shutvik [7]3 years ago

3 0

Answer:

y= 1/3 x +5

Step-by-step explanation:

To find the slope, we take two points

(0,5) and (15,10)

The slope is found by the formula

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

= (10-5)/(15-0)

= 5/15

= 1/3

The slope is 1/3

The y intercept is found when x=0

When x=0 y=5

The slope intercept form of the line is

y=mx+b where m is the slope and b is the y intercept

y= 1/3 x +5

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tester [92]

$\bf \begin{array}{cccccclllll}
\textit{direct proportional variation}\\\\\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
\\
&& y={{ k }}x
\end{array}\\ \quad \\$

$\bf \textit{inverse proportional variation}\\\\
\begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
\\
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\end{array}$

$\bf \\\\
-------------------------------\\\\
\textit{z varies directly with x}\implies z=kx
\\\\
\textit{and inversely with y}\implies z=\cfrac{kx}{y}
\\\\\\
\textit{we also know that}\quad 
\begin{cases}
x=6\\
y=2\\
z=15
\end{cases}\implies 15=\cfrac{k\cdot 6}{2}\implies 30=6k$

$\bf \cfrac{30}{6}=k\implies \boxed{5=k}\impliedby \textit{constant of variation}
\\\\\\
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-------------------------------\\\\
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x=4\\
y=9
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