How to determine random points on a linear slope?

[boarderx]

I'm trying to determine unknown y values of a slope.

The graph starts at point (0,0). There are 18 points on the x-axis (months). At point 18, the value of y = 1,450,196,654 (dollars) - so the known point is (18, 1450196654).

The slope is constant, so I assume I should use a slope of 1.

How can I determine the value of y across the other 17 months? For example, what is the value of y at point 5 on the x-axis? I need all of these points. (1, ?), (2, ?) ... (17, ?)

I first tried using the formula y - y1 = m(x - x1);
So, (y - 1450196654) = 1(x - 18).
But, I don't know what to do once I determine that equation.

Thanks,
Brian

 

[mmm4444bot]

… The slope is constant, so I assume I should use a slope of 1 …

Hi Brian:

The slope is not 1.

(All straight lines have a constant slope.)

The following equation is called the Point-Slope form of a line.

y - y1 = m(x - x1)

Before we use it, we need to know values for m, x1, y1.

You've got the (x1, y1) part.

You're missing the m part.

There is a different formula for calculating the value of m. It's called the Slope formula.

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

We use it, when we know the coordinates of two points.

You actually know two points because one is (0, 0).

Calculate the difference of the two y-coordinates (y2 - y1).

Calculate the difference of the two x-coordinates (x2 - x1)

Slope is the ratio of the difference in y over the difference in x.

Once you know the slope m, go back to the Point-Slope form.

Cheers

MY EDITS: Resolved ambiguous statement and corrected spelling errors

 

[galactus]

Just because it has a constant slope does not mean the slope is 1. The slope is rise over run. The difference in the y values divided by the difference in the x values. \(\displaystyle m=\frac{y-y_{1}}{x-x_{1}}\)

Two points are given for which to find the equation of the line. (18, 1450196654) and (0,0)

Using slope intercept-form, y=mx+b, we can find the slope, m, like so:

\(\displaystyle m=\frac{1450196654-0}{18-0}=\frac{725098327}{9}\approx 80566480.778\)

The slope is a little more than 1, huh?.

Since it passes through the origin, the y-intercept, b, is 0

So, the line equation is \(\displaystyle y=\frac{725098327}{9}x\)

Just plug in the various x (months) values to find y (dollars).

For instance, at x=5, y=402832403.889

 

[mmm4444bot]

… All straight lines have a constant slope…

Darn it! (Another misstatement.)

I should write the following, instead.

"All non-vertical straight lines have a constant slope."

 

[boarderx]

Thanks so much for the assistance! The explanations really helped. I was able to plot all of the points I needed for my charts.

-Brian