write an equation in standard form for the line described. through (6,9), perpendicular to 5x+y=9

Question

Having Issues solving this one.

Answer 1

The problem gives the equation of a line in Standard Form (Ax+By=C).

 

Now, convert this, once and forever, into slope-intercept form (y=mx+b) and find that the slope, m=-A/B.

 

The slope of all lines perpendicular to this line have slope of -1/m (that is, the negative reciprocal). So, their equations are:

    Bx-Ay=D and we need a point to find D.

 

Given the line: 5x+y=9

   the slope m=-5

   The slope of all perpendicular lines is m=1/5 and their equations are:

               x -5y = D

          and we need a point to determine D.    The point is:  (6,9)

             6 - 5(9) = D

              6 - 45 = D

                -39 = D

 

The equation of the perpendicular line (in Standard Form) is:

           x - 5y = -39

Answer 2

Hi Monica, the slope of a line perpendicular to another line is: m₁ = -1/m₂ or it is the negative reciprocal of the other line.

 

Given: 5x + y = 9

 

This equation is in standard form. The slope of a line in standard form is: -a/b. For the given line, the slope is: -5/1 or -5.

 

The slope of a line parallel to the given line is: m₁ = -1/m₂ or m₁ = -1/-5, which equals: 1/5.

 

Using the given point and the slope we just found, use the point-slope form of the line to find the line that is parallel to the given line through the point: (6, 9)

 

Point-slope form of the line:

 

y - y₁ = m * (x - x₁)

 

Substitute:

 

y₁ = 9

 

x₁ = 6

 

m = 1/5

 

y - 9 = 1/5 * (x - 6)

 

To make this simpler, clear the fraction by multiplying the entire equation by 5:

 

5 * (y - 9) = 1/5 * (x - 6)

 

5y - 45 = 1 * (x - 6)

 

Clear the parenthesis:

 

5y - 45 = x - 6

 

Subtract x from both sides:

 

-x + 5y - 45 = -6

 

Add 45 to both sides:

 

-x + 5y = 39

 

Multiply the entire equation by -1:

 

-1 * (-x + 5y = 39)

 

The line parallel to the given line in standard form is:

 

x - 5y = -39

 

Does the point (6, 9) fall on the line? Substitute for x, y in the new line:

 

6 - 5 * 9 = -39

 

6 - 45 = -39

 

-39 = -39, values check.

 

Questions?