Write and solve the equation for the direct variation y varies directly with x if y=112

Question

when x=16
. Find the value of y when x=11
.(1 point)
Responses

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

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=117
.

Answer 1

To solve this problem, we start by noting the direct variation relationship, which can be described by the formula:

\[ y = kx \]

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

1. Find the value of \( k \) using the given information that \( y = 112 \) when \( x = 16 \).

   \[ 112 = k \cdot 16 \]

   Now we can solve for \( k \):

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

2. Now we have the equation for direct variation:

   \[ y = 7x \]

3. Next, find the value of y when \( x = 11 \):

   \[ y = 7 \cdot 11 = 77 \]

So, the correct response is:

When \( x = 11 \), \( y = 77 \).