How to Compute the Point Slope?

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 $$x$$?

• You have the $\ x-$ and $\ y-$values swapped when you entered them into the slope ratio: it should be $\ \frac{20 - 1}{5000 - 125} \ \ .$ If you use desmos.com, and enter the equation $\ y - c \ = \ m·(x-a) \ \$ in the plotter, it will offer you "sliders" with which you can vary the values of the unspecified constants. Sep 27, 2021 at 4:14

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 $$\frac{19}{4875}$$.
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.