Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Halle la ecuación de la recta que es perpendicular a la recta y=2x+1 y pasa por el punto (-2,7)

Halle la ecuación de la recta que es perpendicular a la recta y=2x+1 y=2 x+1 y pasa por el punto (−2,7) (-2,7)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find derivatives using the quotient rule Iright chevron icon

Full solution

Q. Halle la ecuación de la recta que es perpendicular a la recta y=2x+1 y=2 x+1 y pasa por el punto (−2,7) (-2,7)
  1. Identify slope: Identify the slope of the given line y=2x+1y = 2x + 1. The slope (m)(m) is 22.
  2. Find perpendicular slope: Find the slope of the perpendicular line. The slope of the perpendicular line is the negative reciprocal of 22, which is −12-\frac{1}{2}.
  3. Use point-slope form: Use the point-slope form of the equation of a line, y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is the point (−2,7)(-2, 7) and mm is −12-\frac{1}{2}.
  4. Substitute point and slope: Substitute the point (−2,7)(-2, 7) and the slope −12-\frac{1}{2} into the point-slope form: y−7=−12(x+2)y - 7 = -\frac{1}{2}(x + 2).
  5. Simplify equation: Simplify the equation: y−7=−12x−1y - 7 = -\frac{1}{2}x - 1.
  6. Convert to slope-intercept form: Add 77 to both sides to get the equation in slope-intercept form: y=−12x+6y = -\frac{1}{2}x + 6.

More problems from Find derivatives using the quotient rule I

Question
Find the derivative of f(x) f(x) .\newlinef(x)=cos⁡(x) f(x) = \cos(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡(x) f(x) = \tan(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 6 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ex f(x) = e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 6 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ln⁡(x) f(x) = \ln(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 6 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡−1x f(x) = \tan^{-1}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 6 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=xex f(x) = x e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 6 months ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=exx f(x) = \frac{e^x}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 6 months ago

Question
Find the derivative of f(x) f(x) . \newline f(x)=e(x+1) f(x) = e^{(x + 1)} \newline f′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=x+3 f(x) = \sqrt{x+3} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 6 months ago

Question
Find the derivative of g(x) g(x). \newline g(x)=ln⁡(2x) g(x) = \ln(2x) \newline g′(x)= g^{\prime}(x) = ______
Get tutor helpright-arrow

Posted 7 months ago

View all (90)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant