a) Yes the slope makes sense, as the players foot length gets larger, their overall height also increases signifying that there is a correlation between foot size and height.
b) The y-intercept occurs when the line "intercepts" the y-axis. It also makes sense because a player that has 25 cm in distance from heel to toe may very likely be 1.55 meters in height. This is probable.
c) The equation of any line is:
y=mx+b (m= slope, b= y-intercept)
The slope of this line can be found by locating two points where the line intersects. I will use points (25.5,1.6) and (26.25,1.7).
The formula to find the slope is (y(2)-y(1)) / (x(2)-x(1)) = m
1.7 - 1.6 / 26.25 - 25.5 = .1/.75 = .13333
This line crosses the y-intercept at about 1.55m
The equation of this line is:
y = .1333 x + 1.55
