Math 1 · Unit 3 · Lesson 3 · part 3 of 9
What each number does: b slides, m tilts
Keep m the same and change only b.
What each number does: b slides, m tilts
Keep m the same and change only b. The line slides straight up or down. It does not tilt, because the steepness is still m. And because they all have the same steepness, these lines never meet: they are parallel. (Same slope means parallel. That is all we need for now; Unit 4 is all about parallel and perpendicular lines.)
Now keep b the same and change only m. Every line still crosses the y-axis at (0, b), so the line tilts around its y-intercept, like a seesaw on a pin. A bigger m is steeper. An m between 0 and 1 is gentle. When m turns negative the line flips direction and falls instead of climbs. And m = 0 is the flat member, y = b.
Change bThe line slides up or down. Same steepness, so parallel to where it was.
Change mThe line tilts around (0, b). Bigger size is steeper, a negative m falls.
Special membersm = 0: the flat line y = b. m = 1: up 1 for each 1 right, the 45-degree line. Large m: steep. m between 0 and 1: gentle.