Question

A linear function that represents the number of hot dogs purchased at a football game is compared to a different linear function that represents the time left in the game. Describe the key features of the functions that are needed to determine if these lines intersect.

Answer 1

The key features needed are the slopes and y-intercepts. If the slope and the y-intercept are the same then there are infinite amounts of intersections. If the slope is the same and the y-intercept is different then they will never intercept. Of the slope and the y-intercept are different, then they will intersect at one point.

Answer 2

Well if y1= m1x + b1

y2 = m2 x + b2

Lines are the same if m1 = m2 and b1 = b2 (they intersect in infinitely many points)
If b1 ≠ b2 and m1 = m2 then lines are parallel and do not intersect
If m1≠ m2 then lines will intersect at one point