Question

Find the equation of the line the line is perpendicular to the graph of x - 5y=6 and contains 2,-10

Answer 1

Answer:  

y + 10  =  - 5 (x - 2)  [point-slope form]  OR

y = - 5 x     [slope-intercept form]

<h2 />

Step-by-step explanation:

Identify the slope of the given line

If we rewrite the equation given, we can easily identify the slope

                 x - 5y = 6

                    - 5y = - x + 6

                        y  = ¹/₅ x  - ⁶/₅

                                ∴ the slope of x - 5y = 6  is  ¹/₅

Find the slope of the perpendicular line  

When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.

                 ⇒  since the slope of this line = ¹/₅

                      then the slope of the perpendicular line (m) =  - 5

Determine the equation of perpendicular line  

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:  

                             ⇒  y - (-10) =  - 5 (x - 2)

                                         ∴  y + 10  =  - 5 (x - 2)

We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

                                   since    y + 10  =  - 5 (x - 2)

                                               y  =  - 5 x

∴ the slope-intercept equation of the perpendicular line is y + 10  =  - 5 (x - 2)  OR  y = - 5 x.

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.