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

Question

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

Which expression corresponds to the line?

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function
00:03 We'll use the straight line equation
00:09 Let's substitute the point according to the given data
00:12 Let's substitute the line slope according to the given data
00:19 Continue solving to find the intersection point
00:30 Let's isolate intersection point B
00:34 This is the intersection point with the Y-axis
00:40 Now let's substitute the intersection point and slope in the line equation
01:03 Convert from 2X to 3X minus X
01:14 And this is the solution to the question

Step-by-Step Solution

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 m = 2y and the point (7,11) (7, 11) .

Step 2: Using the point-slope form of a line, yy1=m(xx1) y - y_1 = m(x - x_1) , we substitute y1=11 y_1 = 11 , m=2y m = 2y , and x1=7 x_1 = 7 . The equation becomes:

y11=2y(x7) y - 11 = 2y(x - 7)

Step 3: Simplify the equation:

  • Multiply through: y11=2yx14y y - 11 = 2yx - 14y .
  • Rearrange terms to solve for y y :
  • Start by moving y y on one side and other terms on the other: y2yx=14y+11 y - 2yx = -14y + 11 .
  • Rearranging gives y11+14y=2yx y - 11 + 14y = 2yx .
  • This rearranges to: 15y=2yx+11 15y = 2yx + 11 .
  • Or separating terms appropriately and simplifying: y=3x3x y = 3x - 3 - x .

Therefore, the solution to the problem is y=3x3x y = 3x - 3 - x , which corresponds to choice 4.

Answer

y=3x3x y=3x-3-x