Find the Parallel Line Equation Through Point (-3, -4)

To solve this problem, follow these steps:

• Step 1: Identify the given line's slope. The given line is $y = 2x - 5$, which has a slope of $2$.
• Step 2: Since the line we want is parallel, it will have the same slope, $m = 2$.
• Step 3: Use the point-slope formula, $y - y_1 = m(x - x_1)$. Given point is $(-3, -4)$.
• Step 4: Substitute $m = 2$, $x_1 = -3$, and $y_1 = -4$ into the point-slope formula:
  $y - (-4) = 2(x - (-3))$
• Step 5: Simplify the equation:
  $y + 4 = 2(x + 3)$
• Step 6: Distribute the $2$:
  $y + 4 = 2x + 6$
• Step 7: Solve for $y$:
  $y = 2x + 6 - 4$
• Step 8: Simplify further:
  $y = 2x + 2$

The corresponding equation of the line parallel to $y = 2x - 5$ and passing through $(-3, -4)$ is $y = 2x + 2$. When compared to the choices given, the correct choice is:

$y=2x+2$