Question

Use the point-slope form equation to solve this problem:
Passing through (3,5) and (3, 2)

Answer 1

The point-slope equation is
\[y - y _{1} = m(x - x _{1})\] where \[(x_{1}, y_{1})\] is any point on the line, and m is the gradient.

To solve this problem, use the gradient formula
\[m = \frac{ y_{2} - y_{1} }{x_{2} - x_{1} }\]
first to find m, then choose either point to plug into the point-slope equation.

Answer 2

I got m to be 0.

Answer 3

Are you sure you got 0 as the gradient? A negative denominator doesn't mean zero, it means... well, you can't divide by 0, so some people would say it means infinity. In this case though, a line with infinite slope would just be a vertical line, right?

Answer 4

A zero denominator, I mean. Sorry for that confusion.

Answer 5

So what am I supposed to put for that?

Answer 6

I was leading you down the wrong path :P
When we have two point that lie on either a horizontal line or a vertical line, it becomes much easier to find the equation! No formulas needed.
If you were to roughly plot the two points, what do you notice about the line?

Answer 7

They would be on the same x-axis

Answer 8

@Tommynaut

Answer 9

So would it be undefined slope?

Answer 10

Yes, they would be on the same vertical line.
Remember, all horizontal lines are of the form y = b, where b is some number;
and all vertical lines are of the form x = a, where a is some number.

So we know our equation is going to look like x = a. The question is, what is a? What can we tell about all the x values on our line?

And yes, the slope is undefined.

Answer 11

So, what did you get as your final answer?