Find the slope of the line that passes through (3, 6) and (7, 7). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

Hey Jaylyn!

For this problem we need to calculate the slope of the line.

Now slope is defined as change in Y divided by change in X, or in other words, Rise/Run

There are a couple of ways to solve this sort of problem to find the slope. My favorite way is to simply graph first, its often helpful to visualize by graphing.

(Edit apparently I cannot upload photos here, I recommend you graph it out yourself here. if this is confusing check out the analytical method below)

Here I graph (3,6) at point A and (7,7) at point B.

Now we can easily identify the slope be simply counting the rise of A to B, which is 1.

The Run, or change in X we can count as just 4!

Thus slope, or Rise/Run = 1/4

Now I like graphing because it is visual and easy to see the solution by just examining the graph. However if you would prefer it is also simple to calculate analytically, in some cases analytically solving is best, for example when points are very far apart on a graph. In order to solve analytically we still use the same idea, finding rise first, then run.

Rise is the absolute change in Y, or the difference between the two points Y value. Thus

Rise = Y value of point B minus Y value of Point A:

Rise = 7 - 6 = 1

Similarly we find Run, or change in X, as

Run = 7 - 3 = 4

therefore slope = Rise/Run = 1/4

And we have the same answer as before

Hope this helps!

Answer 2

Hi Jaylyn,

Points: (3,6) (7,7)

Here we'll want to use the slope formula : m = (y2-y1)/(x2-x1)

y2 is the y coordinate in the second point. y1 is the y coordinate in the first point.

m = (y2-y1)/(x2-x1)

m = (7-6)/(7-3)

m = 1/4