How to Compute the Point Slope?

Question

Assume I have points $(125,1)$ and $(5000,20)$. The slope would be $m = \frac{y_2 - y_1} { x_2 - x_1}$ or $256.5789474$, right?

Assume the slope and one point are known, I should be able to compute the y value for a given $x$ using the point slope formula $y - y_1 = m (x - x_1)$, right? Using the example above, say I have point $(125,1)$ and a slope of $256.5789474$, what would be $y$ value when $x = 5000$? Should be $20$, right? $$y - y_1 = m (x - x_1) $$ $$y = m (x - x_1) + y1$$ $$ y = 256.5789474 (5000 - 125) + 1$$ $$ y = 1250823.36857$$

What did I do wrong?

Also, are there any online interactive graphing tools that display a slope and allow the user to interact with it to see the different values of $y$ for a given $x$?

Answer 1

So, first, since you are asking for interactive graphing tools. You can use Desmos. https://www.desmos.com/?lang=en

I looked at your question, and I noticed that you got the slope wrong. You did $$\frac{x_{2}-x_{1}}{y_{2}-y_{1}}$$ instead of $$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$ . So, if you have done the slope correctly, you will get m=0.003897 or $$\frac{19}{4875}$$.

The point slope formula is for calculating the equation of a line, but not finding y-values or x-values; it is simply about substitute a point and a slope into the equation and find the equation of the line.

With the question, I will use (125,1) and the slope m= $$\frac{19}{4875}$$ to calculate the line.

$$y-y_{1} = m(x-x_{1})$$ $$y-1 = \frac{19}{4875}(x-125)$$ $$y= \frac{19}{4875}x+ \frac{20}{39}$$ This is the equation of the line.

Then, you can try points out to verify if you have done it correctly, for example, you try (125, 1) or you can try (5000, 20). I have tried them out, and this is correct.