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

Question

Which algebraic equation represents a straight line that passes through the point (3,14) (3,14) and creates an angle of 135 degrees with the positive part of the x axis?

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function
00:03 We'll use the formula to calculate slope based on the angle with X-axis
00:07 We'll substitute the angle according to the given data and calculate to find the slope
00:16 This is the line's slope
00:19 Now we'll use the line equation
00:24 We'll substitute the point according to the given data
00:30 We'll substitute the slope and solve to find the intersection point (B)
00:42 We'll isolate the intersection point (B)
00:47 This is the intersection point with the Y-axis
00:57 Now we'll substitute the intersection point and slope in the line equation
01:16 We'll arrange the equation
01:22 And this is the solution to the question

Step-by-Step Solution

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∘)=tan⁡(135∘−180∘)=tan⁡(−45∘)=−1 m = \tan(135^\circ) = \tan(135^\circ - 180^\circ) = \tan(-45^\circ) = -1 .
Step 2: Using the point-slope formula y−y1=m(x−x1) y - y_1 = m(x - x_1) with (x1,y1)=(3,14)(x_1, y_1) = (3, 14) and m=−1 m = -1 , we have:
y−14=−1(x−3) y - 14 = -1(x - 3) .
Simplifying, y−14=−x+3 y - 14 = -x + 3 .
Rearranging terms gives y=−x+17 y = -x + 17 , or equivalently y+x=17 y + x = 17 .

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

Answer

y+x=17 y+x=17

More Questions

Related Subjects

Finding a Linear Equation

Question Types

Equation of a Straight Line: Using the angle formed by the line with the axes