Find the Equation of Line Parallel to y=2x+5 Through Point (4,9)

Given the line parallel to the line $y=2x+5$

and passes through the point $(4,9)$.

Which of the algebraic representations is the corresponding one for the given line?

To solve this problem, let's proceed through these steps:

• Step 1: Identify the slope of the original line. From $y = 2x + 5$, the slope $m$ is $2$.
• Step 2: Since parallel lines have the same slope, the line we're looking for will also have a slope of $2$.
• Step 3: Use the point-slope formula with the given point $(4, 9)$:

We begin with the point-slope formula:

$y - y_1 = m(x - x_1)$

Substitute $m = 2$, $x_1 = 4$, and $y_1 = 9$ into the equation:

$y - 9 = 2(x - 4)$

Simplify the equation:

$y - 9 = 2x - 8$

Solving for $y$, we obtain:

$y = 2x - 8 + 9$

$y = 2x + 1$

Therefore, the algebraic representation of the line parallel to $y = 2x + 5$ that passes through $(4, 9)$ is:

$y = 2x + 1$