# Equation of a Line - Point-Slope Form

This is the original page for the point-slope form for the equation of a line. All this information plus more can be found on our new point-slope form page. You can find that page by clicking here. There is a link back to this original page on the new page.

y = m(x - x 1 ) + y 1      or      y - y 1 = m(x - x 1 )

Above is a program that will help you visualize how changing the values for the point, (x1, y1), and for the slope, m, will affect the graph of the equation y = m(x - x1) + y1. At first the program will be automatically cycling through several values for x1, y1, and m. If you want to use the sliders to control the program yourself, just press the 'You Control' button.

Notice the point, shown as a little square, which moves around the graph. That point is (x1, y1). The point-slope form equation gets its name from the fact that if you know one point on the line, (x1, y1), and the slope of the line, m, then you can determine, or draw, the line completely.

Experiment with controlling the program yourself. You should be able to realize that any line which you can imagine on the x, y plane can be drawn knowing only one point on the line and the slope of the line.

Summary of Details

This linear function:

f(x) = m(x - x1) + y1

May be graphed on the x, y plane as this equation:

y = m(x - x1) + y1

This equation is often also written as:

y - y1 = m(x - x1)

• This equation is called the point-slope form for a line.
• The graph of this equation is a straight line.
• A known point on the line is (x1, y1).
• The slope of the line is m.

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