Question

Write and solve the equation for the direct variation y varies directly with x if y=112
when x=16
. Find the value of y when x=11
.(1 point)
Responses

When x=11
, y=77
.
When x equals 11 , y equals 77 .

When x=11
, y=117
.
When x equals 11 , y equals Start Fraction 11 over 7 End Fraction .

When x=11
, y=7
.
When x equals 11 , y equals 7 .

When x=11
, y=162.8
.

Answer 1

In a direct variation, we can express the relationship between \( y \) and \( x \) as \( y = kx \), where \( k \) is the constant of variation.

We know that when \( x = 16 \), \( y = 112 \). We can use this information to find \( k \):

\[
y = kx
\]
\[
112 = k(16)
\]

Now, solve for \( k \):

\[
k = \frac{112}{16}
\]
\[
k = 7
\]

Now we have the equation of the direct variation:

\[
y = 7x
\]

Next, we want to find the value of \( y \) when \( x = 11 \):

\[
y = 7(11) = 77
\]

Thus, when \( x = 11 \), \( y = 77 \).

So the final answer is:

**When x equals 11, y equals 77.**