radius; another word for the bone that connects the elbow and wrist. don't get this confused with the radius of a circle, this has NOTHING to do with that...
A woman with an arm radius of 22 centimets long should be about 160 centimeters tall.
A woman with a radius of 26 centimeters long should be about 174 centimeters tall..
- Write a linear equation relating height (y) to the length of the radius (x).
x = radius
y = height
(22,160)
(26,174)
(y-Y1)/(x-X1) = (Y2-Y1)/(X2-X1) (two ways of writing the slope of our line)
(y -160)/(x-22) = (14)/(4) = 7/2
2 y - 320 = 7 x - 154
2 y = 7 x + 166 done
------------------
check a point (22,160)
2 y = 7(22)+166
2 y = 320
y = 160 check
okay, but where is the linear equation?
2 y = 7 x + 166 done
Right there
If you want y = mx + b divide both sides by 2
y = (7/2)x + 83
To write a linear equation relating height (y) to the length of the radius (x), we can use the given information about arm radius and height for two different women. Let's assign the variable x to represent the length of the radius and the variable y to represent the height.
Given that the length of the radius (x) for the first woman is 22 centimeters and her height (y) is 160 centimeters, we have one point (22, 160). For the second woman, with a radius (x) of 26 centimeters and a height (y) of 174 centimeters, we have another point (26, 174).
To find the equation of a line, we can use the point-slope formula:
y - y1 = m(x - x1),
where m is the slope and (x1, y1) is any point on the line. Using the first point (22, 160) as (x1, y1), we can substitute it into the formula:
y - 160 = m(x - 22).
Next, we need to find the slope (m) using the second point (26, 174). The slope is calculated as:
m = (y2 - y1) / (x2 - x1),
m = (174 - 160) / (26 - 22),
m = 14 / 4,
m = 3.5.
Now we have the slope, we can substitute it into the equation to get:
y - 160 = 3.5(x - 22).
Simplifying further, we can distribute 3.5 on the right-hand side:
y - 160 = 3.5x - 77.
Finally, we can isolate y by adding 160 to both sides:
y = 3.5x - 77 + 160.
Simplifying the equation gives:
y = 3.5x + 83.
Therefore, the linear equation relating height (y) to the length of the radius (x) is y = 3.5x + 83.