please help me on this

Question

Find the equation of the line passing through the point left parenthesis minus 2 comma 5 right parenthesis that is perpendicular to the line 6 x plus 2 y equals 8 .

Answer 1

Find the equation of the line that passes through (-2, 5), and is perpendicular to the line ... 6x + y = 8

 

First, lints find the slope of the given line, by writing the equation in slope-intercept form ... y = mx + b

When written in this form, the slope of the line is "m".

 

   6x + y = 8

  

Adding "-6x" to both sides of the equation, gives us

 

   y = -6x + 8

 

Thus the slope of our line is "-6", 

 

The slope of the line that is perpendicular to our line, has a slope that is the negative reciprocal of our line.

So if we take -6, change the sign, and take the reciprocal, we end up with a 1/6 ... the product of the slopes of lines that are perpendicular, is "-1" ... thus the slope of the perpendicular line is 1/6

 

We can now use the point-slope formula, because we have a point on the line, and we have the slope of the line.

 

  y - y₁ = m(x - x₁)

  y - 5 = (1/6)(x -(-2))

  y - 5 = (1/6)(x + 2)

  y - 5 = (1/6)(x) + (1/6)(2)

  y - 5 = (1/6)x + 2/6

  y - 5 = (1/6)x + 1/3

       y = (1/6)x + 1/3 + 5

       y = (1/6)x + 1/3 + 15/3

       y = (1/6)x + 16/3

 

CHECK:  when we plug the point (-2, 5) into the line, we should get a true statement

 

       y = (1/6)x + 16/3

       5 = (1/6)(-2) + 16/3

       5 = -2/6 + 16/3

       5 = -1/3 + 16/3

       5 = 15/3

       5 = 5

 

       TRUE