Question

2) if y varies inversely with x find the constant of variation with x=5 and y=10

3) If y varies directly with x and y =35 when x=5 find x when y=7

4) If y varies directly with x and y =-12 when x=6 find x when y=-4

5) If y varies inversely with x and y and y=8 when x=10 find x when y=4

6) If y varies inversely with x and y and y=-5 when x=20 find x when y=-4

Answer 1

2) if y varies inversely with x find the constant of variation with x=5 and y=10

 k=xy=5x10=50

3) If y varies directly with x and y =35 when x=5 find x when y=7 
 y=1

4) If y varies directly with x and y =-12 when x=6 find x when y=-4 
 x=2

5) If y varies inversely with x and y and y=8 when x=10 find x when y=4
 x=5

6) If y varies inversely with x and y and y=-5 when x=20 find x when y=-4 
 x=16

Answer 2

Part 2) if y varies inversely with x find the constant of variation with x=5 and y=10

we know that
y=k/x
where
k is the constant of variation
x=5  and y=10

10=k/5----> k=50

the answer Part 2) is k=50

Part 3) If y varies directly with x and y =35 when x=5 find x when y=7 
y=k*x
x=5  y=35
35=k*5----> k=35/5----> k=7
so
y=7*x
when y=7
7=7*x------> x=1

the answer Part 3) is x=1

Part 4) If y varies directly with x and y =-12 when x=6 find x when y=-4 
y=k*x
x=6   y=-12
-12=k*6-------> k=-2
so
y=-2*x
when y=-4
-4=-2*x----> x=2

the answer part 4) is x=2

Part 5) If y varies inversely with x and y and y=8 when x=10 find x when y=4
y=k/x
x=10  y=8
8=k/10-----> k=80
so
y=80/x
when y=4
4=80/x----> x=80/4-----> x=20

the answer Part 5) is x=20

Part 6) If y varies inversely with x and y and y=-5 when x=20 find x when y=-4 
y=k/x
x=20   y=-5
-5=k/20----> k=-100
so
y=-100/x
when y=-4
-4=-100/x----> x=100/4----> x=25

the answer Part 6) is x=25