Write an equation for the line

Question

Write an equation for the line perpendicular to -5x+y=5, through (5,5) in slope-intercept form. 

Answer 1

Give the equation of a line in Standard Form (Ax + By = C), the slope m=-A/B and all perpendicular lines have slope B/A (the negative reciprocal).

 

The slope-intercept form of the equation of a line is:  y=mx + b

 

The perpendicular line we seek is:  y = (1)/(-5)x + b          and we need point (5,5) to determine b.

          y = -(1/5)x + b

         5 = -(1/5)(5) + b

         5 = -1 + b

         6 = b

 

The equation of the perpendicular line in slope-intercept form is:   y = -(1/5)x + 6

Answer 2

Equation of the given line is -5x+y=5.

Rewrite this in the slope-intercept form as y=5x+5 (y=mx+c)

So, m₁=5 is the slope.

 

Product of slopes of perpendicular lines = -1

m₁m₂=-1

Therefore, Slope of the second line, m₂ = -1/m₁ = -1/5 = -0.2

 

Equation of a line with slope m₂ passing through (x₁, y₁) is

(y-y₁)=m₂(x-x₁)

Replacing (x₁,y₁) with the coordinates of the given point (5,5),

y-5 = (-1/5) * (x-5) = -0.2x + 1

regrouping, we get

   y = -0.2x+6 as the equation of the second line in slope-intercept form.

 

Answer 3

First task is to determine the slope of the given line.

 

Solve for y to place in slope-intercept form: y = 5x + 5. This line has a slope of 5. 

 

That means any line perpendicular to that one will have a slope of -1/5 (negative reciprocal).

 

Since the line must pass through (5,5), we can use point-slope (at least that is one option) to write:

 

y-5 = -1/5(x - 5)  (from this point there are a few choices--I would picture multiplying both sides of the equation by 5 to remove the fraction.

 

5y - 25 = -1(x-5)

5y - 25 = -x + 5

 

5y = -x +30

 

y = -1/5(x) + 6 (slope-intercept form)