Can someone help me with the slope formula?

Question

anonymous · Answer

Sure, what's the issue?

quickstudent · Answer

I know that the formula is  (m) = (y2−y1)/(x2−x1).
The points on the line are (15, 5), (30, 10).

When I plugged them in, my answer was 3.
But when I checked my answer with a slope calculator, it said the answer was 1/3.

anonymous · Answer

Okay. Let's say that $$\left( x_1,y_1 \right)=\left( 15,5 \right) \text{ and } \left( x_2,y_2 \right) = \left( 30,10 \right)$$BTW, it doesn't matter which you choose as point 1 and point 2...you'll get the same answer.
Now, apply the slope formula$$m=\frac{ y_2-y_1 }{ x_2-x_1 }=\frac{ 10-5 }{ 30-15 }=?$$

quickstudent · Answer

Oh, in that case it will be 1/3. I put 30-15 at the top.

anonymous · Answer

Great. Remember that, in an ordered pair, the x-coordinate is first, then the y-coordinate.

quickstudent · Answer

But how do I know which pair should be the numerator and denominator in the formula?

quickstudent · Answer

@ospreytriple

quickstudent · Answer

Oh, wait, now I get it

quickstudent · Answer

Yes, I put the x values as the numerator of the formula. That was my mistake. Y goes at the top, x at the bottom.

anonymous · Answer

As you've stated above, the slope formula is$$m=\frac{ y_2-y_1 }{ x_2-x_1 }$$Therefore the y-coordinates are used in the numerator and the x-coordinates are used in the denominator.

quickstudent · Answer

Great. I understand completely now. Thanks!