Find the Linear Equation: Line Through Point (3,14) at 135 Degrees

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

• Step 1: Calculate the slope
• Step 2: Apply the point-slope form to get the line equation
• Step 3: Simplify and verify against given choices

Now, let's work through each step:
Step 1: The slope for a line making 135 degrees with the x-axis is $m = \tan(135^\circ) = \tan(135^\circ - 180^\circ) = \tan(-45^\circ) = -1$.
Step 2: Using the point-slope formula $y - y_1 = m(x - x_1)$ with $(x_1, y_1) = (3, 14)$ and $m = -1$, we have:
$y - 14 = -1(x - 3)$.
Simplifying, $y - 14 = -x + 3$.
Rearranging terms gives $y = -x + 17$, or equivalently $y + x = 17$.

Therefore, the equation of the line is $y + x = 17$.