find the general equation of the line with y- intercept equal to 8 and perpendicular to the line 2x + y - 10 = 0

Question

parallel and perpendicular

Answer 1

The General Form of the equation of a line looks like:   Ax + By + C = 0

 

Now, if you, once and forever, you convert that to the slope-intercept form of the equation of a line (y = mx + b), you will find that:

     the slope, m, is (-A/B)

     the y-intercept (the place where x=0) is the point (0,-C/B)

 

Now, you should realize that perpendicular lines have slopes that are the negative reciprocal of each other.  So, slopes of m and (-1/m) fit this description.  That is, the slope of the line we want is (B/A).  So, it has this equation:

    x - 2y + C₁ = 0                [note: different C]

 with a y-intercept of

     -C₁/B = 8        [given]

       C₁ = 16        [since B=-2]

 

That makes the equation of the perpendicular line (in General Format):     x - 2y + 16 = 0

Answer 2

The slope intercept form is

y = mx+b where m is the slope

and b is the y-intercept so we have

 

y = mx + 8

 

The line perpendicular to 

2x + y - 10 = 0

will have a slope that is the

negative reciprocal of the slope 

of this line... m_⊥ = -1/m

 

2x + y = 10

y = -2x + 10

m = -2

m_⊥ = -1/-2 = 1/2

 

y = (1/2)x + 8 is your equation