Find the Equation of a Line Passing Through (3,7) with a Slope of 2y

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

• Step 1: Write the equation using point-slope form
• Step 2: Substitute the given point and slope into the equation
• Step 3: Simplify to find the slope-intercept form of the line equation

Now, let's work through each step:

Step 1: Use the point-slope form of a line equation, given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line.

Step 2: Given that the slope is represented as $2y$ and the line passes through point $(3, 7)$, we should interpret it as the slope being equivalent to 2 (as $2y$ in relation suggests $y=2x+b$ structure supposedly intended this way). This gives us a slope $m = 2$.

Using point $(3, 7)$, we substitute into the formula:

$y - 7 = 2(x - 3)$

Step 3: Simplify the equation:

$y - 7 = 2x - 6$

$y = 2x - 6 + 7$

$y = 2x + 1$

Therefore, the equation of the line is $y = 2x + 1$.