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What does y=mx mean? Where does it come from?

Learn how the equation y=mx is derived using similar triangles and how it represents the slope of a line. Understand why the ratio of rise to run is constant in any line. Explore examples and apply the concept to solve slope-related questions.

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What does y=mx mean? Where does it come from?

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  1. What does y=mx mean? Where does it come from?

  2. In this lesson you will learn to derive the equation y=mx by using similar triangles.

  3. For any line, the ratio of rise to run is constant. 6 9 We call this ratio the slope of the line. 4 6 Slope = = =

  4. Be careful! Slope = Slope =

  5. Slope: x (x, y) 3 y 2 (0, 0) = y = x

  6. x Slope: m (x, y) 1 y m (0, 0) = y = mx

  7. Any point (x,y) on a line through the origin with slope m will satisfy y=mx. y=mx is the equationof a line through the origin with slope m.

  8. In this lesson you have learned to derive the equation y=mx by using similar triangles.

  9. Use similar triangles to demonstrate that the equation of a line through the origin with slope 3 is y=3x.

  10. A line through the origin has slope . Does it pass through (8,10)? Explain.

  11. A line through the origin passes through (5,6). What is the line’s equation?

  12. Use similar triangles to demonstrate that the equation of a line through the origin with slope is y=x.

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