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?

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function

00:03 This is the slope of the line

00:08 Parallel lines have identical slopes

00:12 Let's use the line equation

00:16 Let's substitute the point according to the given data

00:25 Let's substitute the line slope according to the given data

00:31 Let's continue solving to find the intersection point

00:37 Let's isolate the intersection point (B)

00:40 This is the intersection point with the Y-axis

00:44 Now let's substitute the intersection point and slope in the line equation

00:57 And this is the solution to the question

Step-by-Step Solution

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:

$y = 2x + 1$