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

When x=11
, y=162.8
.
When x equals 11 , y equals 162.8 .

When x=11
, y=117
.

1 answer

In direct variation, we can express the relationship between \( y \) and \( x \) as:

\[ y = kx \]

where \( k \) is the constant of variation.

Given that \( y = 112 \) when \( x = 16 \), we can find \( k \):

\[ 112 = k(16) \]

To find \( k \), we solve for it:

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

Now, we know the relationship:

\[ y = 7x \]

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

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

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

The correct response is:

When x=11, y=77.