Find the Line Equation: Passing Through (7,11) with Slope 2y

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function

00:03 We'll use the straight line equation

00:09 Let's substitute the point according to the given data

00:12 Let's substitute the line slope according to the given data

00:19 Continue solving to find the intersection point

00:30 Let's isolate intersection point B

00:34 This is the intersection point with the Y-axis

00:40 Now let's substitute the intersection point and slope in the line equation

01:03 Convert from 2X to 3X minus X

01:14 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Now, let's work through each step:

Step 1: The problem gives us the slope $m = 2y$ and the point $(7, 11)$ .

Step 2: Using the point-slope form of a line, $y - y_1 = m(x - x_1)$ , we substitute $y_1 = 11$ , $m = 2y$ , and $x_1 = 7$ . The equation becomes:

$y - 11 = 2y(x - 7)$

Step 3: Simplify the equation:

Multiply through: $y - 11 = 2yx - 14y$ .
Rearrange terms to solve for $y$ :
Start by moving $y$ on one side and other terms on the other: $y - 2yx = -14y + 11$ .
Rearranging gives $y - 11 + 14y = 2yx$ .
This rearranges to: $15y = 2yx + 11$ .
Or separating terms appropriately and simplifying: $y = 3x - 3 - x$ .

Therefore, the solution to the problem is $y = 3x - 3 - x$ , which corresponds to choice 4.