Question

A direct variation includes the points (6, 18) and (n, -3). Find n.

Answer 1

To find the value of n in a direct variation with points (6, 18) and (n, -3), we set up the equation 18/6 = -3/n which simplifies to n = -1.

Step-by-step explanation:

To find the value of n when a direct variation includes the points (6, 18) and (n, -3), we must recognize that in a direct variation, the ratio of the y-values to the x-values is constant. That is, if two points (x1, y1) and (x2, y2) are on the line, then y1/x1 = y2/x2.

In this case, we have the points (6, 18) and (n, -3). Thus, we can set up the equation 18/6 = -3/n. This simplifies to 3 = -3/n. To solve for n, multiply both sides of the equation by n to get 3n = -3. Then divide by 3 to solve for n, which gives us n = -1.

Therefore, the value of n that we're looking for is -1.

Answer 2

Since we have a direct variation, we can use the following equation:

`(y)/(x)=k`

where k is the constant of variation.

If we use the point (6,18), then, we have:

`\begin{gathered} (x,y)=(6,18) \\ \Rightarrow(18)/(6)=k \\ \Rightarrow k=3 \end{gathered}`

now that we have that the constant of variation is k = 3, we can use this information to find n:

`\begin{gathered} (x,y)=(n,-3) \\ k=3 \\ \Rightarrow-(3)/(n)=3 \\ \Rightarrow-3=3\cdot n \\ \Rightarrow n=-(3)/(3)=-1 \\ n=-1 \end{gathered}`

therefore, n = -1