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

A straight line with a slope of 2 passes through the point $(7,11)$.

Which expression corresponds to the line?

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

• Step 1: Identify the given information.
• Step 2: Apply the point-slope formula.
• Step 3: Simplify to match one of the given options.

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.