Answer:
[tex]\textsf{2.} \quad y=\dfrac{35}{x}[/tex]
[tex]\textsf{3.} \quad y=-\dfrac{90}{x}[/tex]
[tex]\textsf{4.} \quad y=\dfrac{63}{x}[/tex]
[tex]\textsf{5.} \quad y=-\dfrac{112}{x}[/tex]
Step-by-step explanation:
If y is inversely proportional to x, then:
[tex]y \propto\dfrac{1}{x} \implies y=\dfrac{k}{x} \quad \textsf{(for some constant }k)[/tex]
Question 2
Substitute one of the given ordered pairs into the inverse variation equation and solve for k:
[tex]\implies 7=\dfrac{k}{5}[/tex]
[tex]\implies 7 \cdot 5=\dfrac{k}{5} \cdot 5[/tex]
[tex]\implies k=35[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:
[tex]\implies y=\dfrac{35}{x}[/tex]
Question 3
Substitute y = -15 and x = 6 into the formula and solve for k:
[tex]\implies -15=\dfrac{k}{6}[/tex]
[tex]\implies -15 \cdot 6=\dfrac{k}{6} \cdot 6[/tex]
[tex]\implies k=-90[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given values:
[tex]\implies y=-\dfrac{90}{x}[/tex]
Question 4
Substitute one of the given ordered pairs into the inverse variation equation and solve for k:
[tex]\implies 9=\dfrac{k}{7}[/tex]
[tex]\implies 9 \cdot 7=\dfrac{k}{7} \cdot 7[/tex]
[tex]\implies k=63[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:
[tex]\implies y=\dfrac{63}{x}[/tex]
Question 5
Substitute one of the given ordered pairs into the inverse variation equation and solve for k:
[tex]\implies -16=\dfrac{k}{7}[/tex]
[tex]\implies -16 \cdot 7=\dfrac{k}{7} \cdot 7[/tex]
[tex]\implies k=-112[/tex]
Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:
[tex]\implies y=-\dfrac{112}{x}[/tex]
Learn more about inverse variation here:
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