The slope intercept form of the equation of a line is explored interactively using an applet. The investigation is carried out by changing parameters m and b in the equation of a line given by:
y = mx + b
Interactive Tutorials
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click on the button above "click here to start" and MAXIMIZE the window obtained.
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Set m to a fixed value (m = 1) and change b (b = 1, 2, 3, 4, -1, -2, -3, -4). Compare each value of b to the y-intercept of the line obtained.
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Set b to a fixed value (b = 1) and change m (m = 1, 2, 3, 4, -1, -2, -3, -4). For each value of m, find two points on the line obtained and use them to calculate the slope of the line. Compare the slope of the line with m.
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Change m and and explore further.
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Set m = 0 and describe the line obtained.
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Describe the geometrical significance of parameters m and b.
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Find a formula (in terms of m and b) for the x intercept of a line whose equation is y = mx + b. Use different values for m and b to check the formula obtained. Can this formula be used when m = 0? Explain.
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Exercises
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Find, analytically, the slope , the x and y intercepts of the line whose equation is given by
y = -2x + 4
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What is the slope and x intercept of the line whose equation is given by y = -3?
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What is the y intercept of the line whose equation is given by y = -x?
- Use the applet to CHECK your answers to questions i, ii and iii.
More references on lines and slopes.
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