Question

Interpret the slope in terms of the situation. Does it make sense?

Interpret the y-intercept in terms of the situation. Does it make sense?



Determine the equation of the line of best fit. Write your answer in slope-intercept form. Any non-integers in this problem should be entered as decimal numbers. Round to three decimal places when necessary.

Answer 1

y = 0.133x - 1.791

Explanation:

The points (27, 1.8) and (27.75, 1.9) lie on the line of best fit. Use these points to find the slope:

m = y2 - y1 1.9 - 1.8 0.1

------------- = ----------------- = -------- = 0.133

x2 - x1 27.75 - 27 0.75

Plug the value of the slope into the equation of the line y = mx +b to get .

y = 0.133x + b

Substitute the point (27, 1.8) into the equation and solve for b:

1.8 = 0.133(27) + b

b = -1.791

Plug the value of b into the equation of the line of best fit to get:

y = 0.133x - 1.791

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This answer came straight from the sample answer on Edmentum.com.

Answer 2

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