Question

A couple quick algebra 1 questions for 50 points!

Answer 1

Answer:

$\textsf{2.} \quad y=\dfrac{35}{x}$

$\textsf{3.} \quad y=-\dfrac{90}{x}$

$\textsf{4.} \quad y=\dfrac{63}{x}$

$\textsf{5.} \quad y=-\dfrac{112}{x}$

Step-by-step explanation:

If y is inversely proportional to x, then:

$y \propto\dfrac{1}{x} \implies y=\dfrac{k}{x} \quad \textsf{(for some constant }k)$

Question 2

Substitute one of the given ordered pairs into the inverse variation equation and solve for k:

$\implies 7=\dfrac{k}{5}$

$\implies 7 \cdot 5=\dfrac{k}{5} \cdot 5$

$\implies k=35$

Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:

$\implies y=\dfrac{35}{x}$

Question 3

Substitute y = -15 and x = 6 into the formula and solve for k:

$\implies -15=\dfrac{k}{6}$

$\implies -15 \cdot 6=\dfrac{k}{6} \cdot 6$

$\implies k=-90$

Substitute the found value of k into the formula to create the inverse variation equation for the given values:

$\implies y=-\dfrac{90}{x}$

Question 4

Substitute one of the given ordered pairs into the inverse variation equation and solve for k:

$\implies 9=\dfrac{k}{7}$

$\implies 9 \cdot 7=\dfrac{k}{7} \cdot 7$

$\implies k=63$

Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:

$\implies y=\dfrac{63}{x}$

Question 5

Substitute one of the given ordered pairs into the inverse variation equation and solve for k:

$\implies -16=\dfrac{k}{7}$

$\implies -16 \cdot 7=\dfrac{k}{7} \cdot 7$

$\implies k=-112$

Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:

$\implies y=-\dfrac{112}{x}$

Learn more about inverse variation here:

brainly.com/question/27953000