Answer:
Part 4) k=1/2
Part 5) k=-2/3
Part 6) y=32
Part 7) x=6
Part 8) v=99
Part 9)b=6
Part 10) y=6
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Part 4) Find the value of the constant of proportionality k
we have
[tex]y=\frac{1}{2}x[/tex]
Remember that the value of k is the same that the value of the slope
[tex]m=\frac{1}{2}[/tex]
so
[tex]k=\frac{1}{2}[/tex]
Part 5) Find the value of the constant of proportionality k
we have
[tex]y=-\frac{2}{3}x[/tex]
Remember that the value of k is the same that the value of the slope
[tex]m=-\frac{2}{3}[/tex]
so
[tex]k=-\frac{2}{3}[/tex]
Part 6) Suppose that y varies directly with x, and y=16 when x=8. Find y when x=16
step 1
Find the value of the constant of proportionality k
[tex]k=y/x[/tex]
[tex]k=16/8=2[/tex]
step 2
Find the equation of the direct variation
[tex]y=kx[/tex]
substitute the value of k
[tex]y=2x[/tex]
step 3
Find y when x=16
[tex]y=2(16)=32[/tex]
Part 7) Suppose that y varies directly with x, and y=21 when x=3. Find x when y=42
step 1
Find the value of the constant of proportionality k
[tex]k=y/x[/tex]
[tex]k=21/3=7[/tex]
step 2
Find the equation of the direct variation
[tex]y=kx[/tex]
substitute the value of k
[tex]y=7x[/tex]
step 3
Find x when y=42
[tex]42=7x[/tex]
solve for x
[tex]x=42/7[/tex]
[tex]x=6[/tex]
Part 8) Suppose that v varies directly with g, and v=36 when g=4. Find v when g=11
step 1
Find the value of the constant of proportionality k
[tex]k=v/g[/tex]
[tex]k=36/4=9[/tex]
step 2
Find the equation of the direct variation
[tex]v=kg[/tex]
substitute the value of k
[tex]v=9g[/tex]
step 3
Find v when g=11
[tex]v=9(11)=99[/tex]
Part 9) Suppose that a varies directly with a, and a=7 when b=2. Find b when a=21
step 1
Find the value of the constant of proportionality k
[tex]k=a/b[/tex]
[tex]k=7/2=3.5[/tex]
step 2
Find the equation of the direct variation
[tex]a=kb[/tex]
substitute the value of k
[tex]a=3.5b[/tex]
step 3
Find b when a=21
[tex]21=3.5b[/tex]
solve for b
[tex]b=21/3.5[/tex]
[tex]b=6[/tex]
Part 10) Suppose that y varies directly with x, and y=9 when x=3/2. Find y when x=1
step 1
Find the value of the constant of proportionality k
[tex]k=y/x[/tex]
[tex]k=9/(3/2)=6[/tex]
step 2
Find the equation of the direct variation
[tex]y=kx[/tex]
substitute the value of k
[tex]y=6x[/tex]
step 3
Find y when x=1
[tex]y=6(1)=6[/tex]
