Question

Which two points did you use to draw the line of best fit?
(60.5, 61), and points (70, 71)

Write the equation of the line passing through those two points using the point-slope formula
y - y1= m(x - x1). Show all of your work. Remember to find the slope of the line first.

Using the equation that you found in question 2, approximately how tall is a person whose arm span is 66 inches?

According to your line of best fit, what is the arm span of a 74-inch-tall person?

Answer 1

Just help on the last three

Answer 2

Find m first:
\[m = \frac{ y_2 - y_1 }{ x_2 - x_1 }\]
use the two (x,y) points you used for the best fit line.

point slope form will only use (x1,y1) and the x and y are left as variables

so it wold be:

y - 61 = m(x - 70) --- with the m you found above plugged in


3rd one:

use that formula to find y [height] when x = 66

4th

use that formula to find x [span] when y = 74

Answer 3

\[\frac{ 20 }{ 19 } ?\]

Answer 4

yes

Answer 5

okay lol how exactly do i plug all that in

Answer 6

well the point-slope form of it is:

\[y - 61 = \frac{ 20 }{ 19 }(x - 70)\]

Answer 7

for 3 and 4 you'll want to plug in either x or y to find what they want to know

Answer 8

:) lmk if you have follow-up questions

Answer 9

Yeah i just a hard to with this whole section lol \[y - 61 = \frac{ 20 }{ 19 } (66 - 70)\]
\[74 - 61 = \frac{ 19 }{ 20 }(x-70)\]

Answer 10

which number (x or y) is arm span ?

Answer 11

x is arm span

Answer 12

The point slope formula is
\[ y -y_1 = m(x-x_1) \]
where \( (x_1,y_1) \) is any point on the line.
we could use the point (70, 71)

(up above it looks like you use (70,61) which is not a point on the line )

you get
\[ y -71 = \frac{20}{19} \left(x - 70\right) \]
you can distribute the 20/19 to get
\[ y -71 = \frac{20}{19}x - \frac{20}{19}\cdot 70 \]
and add +71 to both sides
\[ y = \frac{20}{19}x +71 - \frac{20}{19}\cdot 70 \]
if we put 71 over the common denominator of 19 (multiply 71 times 19/19), you get
\[ y = \frac{20}{19}x + \frac{71\cdot 19}{19} - \frac{20\cdot 70 }{19}\]
now simplify the fraction. The numerator is
71*19 - 20*70= 1349- 1400 = -51
the denominator stays 19

your equation in slope-intercept form is
\[ y = \frac{20}{19}x - \frac{51}{19} \]

Answer 13

now you can find the height (y) for arm span (x) = 66

\[ y = \frac{20}{19} \cdot 66 - \frac{51}{19} \]

and to find the arm span when the height y=74
\[ 74= \frac{20}{19} x - \frac{51}{19} \]
if we multiply both sides (and *all* terms by 19, you get
\[ 74 \cdot 19= 20 x - 51 \]
add 51 to both sides
\[ 74 \cdot 19+51= 20 x \]
now divide both sides and *all terms* by 20
\[ \frac{74\cdot 19+51}{20} = x \]
or
\[ x = \frac{74\cdot 19+51}{20} \]