y - y1 = m(x - x1)

The formula y - y1 = m(x - x1) is usuallydescribed as the "point-slope form" for theequation the a line.

You are watching: Y=m(x-x1)+y1

It is useful because if you know one point on a particular line and also theslope of that certain line, then you can specify the line with this form offormula and, thus, find all the other points ~ above that certain line.

Where is the point?

To use this equation you need to know one suggest on a details line. Thename the this known suggest is (x1, y1), and these x- and y-coordinate valuesare the numbers the appear, respectively, as x1and y1 in the equation. Listed below the known suggest isshown by the yellow dot, and also it has the collaborates (2, 5).


Where is the slope?

The slope of the line is the change m. Listed below the slopeof our heat is calculated with a climb of 15 and also a run of 5. The steep isequal come 3.


And the equation in suggest slope form is....


The following interactive application

The program below lets you readjust the known point coordinates and theslope for a line. You will have the ability to see how these transforms effect thepoint-slope equation the the line, i beg your pardon is displayed over the graph, upperleft.

This is one EZ math Movie. Click the "Show system" checkbox to expose theEZ mathematics Movie language. You do not have to understand EZ mathematics Movie come usethis application.

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OptionsInOutGraphPrintBeforeLoopAfter" title="Runs the program">" title="Resumes the program after a pause">
Graph x:<-10, 10>, y:<-10, 10>" title="Starts the prior to loop code">" title="Resumes the loop password cycling">Bounds: x:<-0.01, 0.01>, y:<-0.01, 0.01>x:<-0.1, 0.1>, y:<-0.1, 0.1>x:<-1, 1>, y:<-1, 1>x:<-10, 10>, y:<-10, 10>x:<-100, 100>, y:<-100, 100>x:<-1000, 1000>, y:<-1000, 1000>x:<-2Pi, 2Pi>, y:<-2, 2>x:<-2Pi, 2Pi>, y:<-10, 10>x:<-2Pi, 2Pi>, y:<-100, 100>x:<-360, 360>, y:<-2, 2>x:<-360, 360>, y:<-10, 10>x:<-360, 360>, y:<-100, 100>
// Prepare graph.setupGraph();// obtain slope from 1st input.m = get1stInputValue();// acquire x-coordinate from 2nd input.x1 = get2ndInputValue();// gain y-coordinate from third input.y1 = get3rdInputValue();// uncover y-interceptb = -(m * x1) + y1;// discover left-most y-coordinate.yLeft = (m * worldXMin) + b;// discover right-most y-coordinate.yRight = (m * worldXMax) + b;// draw line from left sheet to ideal edge.drawLineSegment(worldXMin, yLeft, worldXMax, yRight);// draw pointdrawPoint(x1, y1);// display slope-intercept form.displayEquation(x1, y1, m);// execute this just once.// go again ~ above input.stop();

Original page

The original page for this information has a Java applet animationthat resembles the application uncovered here. If your browser runs Java, youmay desire to take a look in ~ it. Girlfriend can discover it byclicking here.


This page has an EZ mathematics Movie application. EZ mathematics Movie is an animation programming language that helps you experiment with mathematics. Learn much more about it at ezmathmovie.com
LabelName: Domain: <-0.01, 0.01> through 0.001<-0.1, 0.1> by 0.01<-1, 1> by 0.1<-10, 10> through 1<-100, 100> by 10<-2Pi, 2Pi> by 0.05Pi<-360, 360> by 5Name0