Write the equation of the line described

Question

The line is perpendicular to y=30 and passes through (4,8)

Answer 1

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

     where m is the slope and b is the y-intercept

 

The equation y=30 is in slope-intercept form.  The slope (m) is 0.     y = 0x +30

 

All lines perpendicular to this line have a slope that is the negative inverse of m.  That is, it is not defined (it is:  -1/0).

 

That means that the slope-intercept form of the equation of a line cannot be used to express it.  However, the Standard Form of the equation of a line can.  The Standard Form of the equation of a line is:   Ax+By=C

     The original line:      0x-1y=-30      or y=30      (slope is -A/B)    (it is horizontal line)

     All parallel lines:     1x+0y=C      x=C  (for every value of y)    (it is a vertical line)

 

The specific vertical line that goes through point (4,8) is:

                            x=4            (note: y can be any value)