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

Video Solution

Solution Steps

00:08 Let's find the algebraic form of the function. Ready?

00:12 We'll use the equation for a straight line.

00:17 First, let's plug in the point from our data.

00:21 Next, substitute the slope from the given information.

00:27 Keep going! Solve to find where the line crosses the Y-axis.

00:38 Focus now on isolating point B, the intersection point.

00:43 This point is where the line intersects the Y-axis.

00:48 Now, substitute both the intersection point and the slope back into the line equation.

01:11 Change two X to three X minus X, as part of the solution.

01:22 And that's how we solve this problem. Great job!

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.