Q. Which graph represents \(y – 1 = 2(x – 4)\)?

We are given the equation in point‑slope form. The goal is to identify the line it represents by converting to a more convenient form and extracting its key features.

Start from the equation in point‑slope form. Convert it to slope‑intercept form by expanding and isolating \(y\).

\[
y – 1 = 2(x – 4)
\]

Distribute on the right side.

\[
y – 1 = 2x – 8
\]

Add \(1\) to both sides to solve for \(y\).

\[
y = 2x – 8 + 1
\]

Combine like terms.

\[
y = 2x – 7
\]

From the slope‑intercept form \(y = 2x – 7\) we read off the slope and the y‑intercept. The slope is \(2\). The y‑intercept is \((0,-7)\).

We can also compute the x‑intercept by setting \(y = 0\) and solving for \(x\).

\[
0 = 2x – 7
\]

\[
2x = 7
\]

\[
x = \tfrac{7}{2} = 3.5
\]

So the line passes through the point \((4,1)\), has slope \(2\) (it rises 2 units for each 1 unit it runs to the right), crosses the y‑axis at \((0,-7)\), and crosses the x‑axis at \((3.5,0)\). Any graph that shows a straight line with these properties (slope \(2\), y‑intercept \(-7\), passing through \((4,1)\)) is the correct graph for the equation \(y – 1 = 2(x – 4)\).