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
click on the button above "click here to start" and MAXIMIZE the window obtained.
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.
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.
Change m and and explore further.
Set m = 0 and describe the line obtained.
Describe the geometrical significance of parameters m and b.
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.
Find, analytically, the slope , the x and y intercepts of the line whose equation is given by
y = -2x + 4
What is the slope and x intercept of the line whose equation is given by y = -3?
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.