Finite Mathematics, Chapter 1, 1.1, Section 1.1, Problem 30

Determine a equation in slope intercept form (where possible) for the line that goes through $(2,-5)$ and parallel to $y - 4 =2x$

If we transform the given line into point slope form, we have

$
\begin{equation}
\begin{aligned}
y - 4 &= 2x \\
\\
y &= 2x + 4
\end{aligned}
\end{equation}
$

Now that the line is in the slope intercept form $y = mx + b$. By observation, $m = 2$
And if the line is parallel to the line we are looking, then we can say that both lines have the same slope
By using the point slope form,the equation of the line will be $y - y_1 = m(x - x_1)$

$
\begin{equation}
\begin{aligned}
y - (-5) &= 2(x - 2)\\
\\
y + 5 &= 2x - 4 \\
\\
y &= 2x - 9
\end{aligned}
\end{equation}
$