Write the transformations using two sets of variables (like $x_G, y_G$ and $x_H, y_H$) so you do not mix up which coordinates belong to which data set.

After finding the line equation for data set G, replace $x_G$ and $y_G$ using expressions in terms of the new coordinates for data set H, then simplify to solve for the new $y$ in terms of the new $x$.

In Desmos, enter the points (2,34) and (10,14).

Define m = (14-34)/(10-2) and note the value Desmos shows for m.

Define b = 34 - m*2 to get the line $y_G = mx_G + b$.

Use the transformations to write old coordinates in terms of new ones:

• xG = (x-4)/2
• yG = 2y+6

Enter the equation yG = m*xG + b (using your definitions for xG and yG). Desmos will graph a line in the $(x,y)$ plane.

Find its $y$-intercept and slope (rise over run) from the graph, then choose the answer option whose intercept and slope match.

From the graph, the line of best fit passes through the labeled points $R(2,34)$ and $S(10,14)$. These two points determine the line for data set G.

Compute the slope:

Use $R(2,34)$ to find the intercept $b$:

So a line of best fit for data set G is $y = 39 - \frac{5}{2}x$.

Let $(x_G, y_G)$ be coordinates in data set G and $(x_H, y_H)$ be coordinates in data set H.

The transformations described give:

Solve each for the old variables in terms of the new ones:

Start with the line for data set G:

Substitute $y_G = 2y_H + 6$ and $x_G = \frac{x_H - 4}{2}$:

Simplify:

Thus an equation of a line of best fit for data set H could be $y = 19 - \frac{5}{8}x$.