SOLUTION: Find the equation of each line in the form y = mx + b if possible. The line through (3, 2) with undefined slope

Algebra ->  Coordinate-system -> SOLUTION: Find the equation of each line in the form y = mx + b if possible. The line through (3, 2) with undefined slope       Log On


   

Question 257314: Find the equation of each line in the form y = mx + b if
possible.
The line through (3, 2) with undefined slope
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The key here is to recognize what "undefined slope" is telling you. The only kind of line that has undefined slope is a vertical line.

Vertical lines are very special and they cannot be handled like other lines. We just have to learn about them:
  • On a vertical line, the x-coordinates of all the points on the line are the same number.
  • Because all the x-coordinates are the same, the slope formula, m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29, has a denominator that works out to be zero. And dividing by zero is undefined. Therefore the slope of vertical lines is undefined.)
  • With an undefined slope, forms like Slope-intercept or Point-Slope cannot be used with vertical lines.
  • Vertical lines have equations of the form:
    x = some-number
    where "some-number" is the number that matches the x-coordinates of all the points on the line.

So once we see that the desired line has undefined slope, we know its equation will be of the form:
x = some-number
And since the point (3, 2) is supposed to be on this line, then the equation is:
x = 3