# Applications of Linear Eqns: x, length of person’s arm in inches and y, height of

#### sean1

##### New member
Applications of Linear Eqns: x, length of person’s arm in inches and y, height of

Hello my friends,
I had to leave this problem blank on my quiz but I have been able to work some of it out on my own (I think.) The part that I am stuck on is how to find b or the y intercept with the information that I have:

The pairs of information (x,y) represent x, the length of a person’s arm in inches and y, the height of the same person in inches. Given (17,58) and (24,82), (a) find a linear equation through the two points. (b) Use the equation to estimate the height of a person whose arm is 21 inches.

I used y2-y1/x2-x1 =
(58-82)/(24-58) = -24/-34 = 12/17
so that gives me y=12/17x+ ??? <--- that is where I am stuck. How do I find b or the y intercept with this information?
Any help is REALLY appreciated, thank you.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello my friends,
I had to leave this problem blank on my quiz but I have been able to work some of it out on my own (I think.) The part that I am stuck on is how to find b or the y intercept with the information that I have:

The pairs of information (x,y) represent x, the length of a person’s arm in inches and y, the height of the same person in inches. Given (17,58) and (24,82), (a) find a linear equation through the two points. (b) Use the equation to estimate the height of a person whose arm is 21 inches.

I used y2-y1/x2-x1 =
(58-82)/(24-58) = -24/-34 = 12/17... incorrect ... m = (82-58)/(24-17) = 24/7
so that gives me y=12/17x+ ??? <--- that is where I am stuck. How do I find b or the y intercept with this information?
Any help is REALLY appreciated, thank you.
Using the second point:

82 = 24/7 * 24 + b

Solve for 'b'.

Last edited:

#### sean1

##### New member
Using the second point:

82 = 24/7 * 24 + b

Solve for 'b'.
Ok, so this is what I have:
82=576/7+b
b+576/7=82
-576/7 -576/7
b= -2/7

b)502/7

Thanks for the help! If only my professor would show a little heart and have these work out to be whole numbers. :cool:

#### HallsofIvy

##### Elite Member
Another way to do this: every (non-vertical) line has equation y= ax+ b. Since the line must go through (17, 58) we must have 58= 17a+ b. Since the line must go through (24, 82) we must have 82= 24a+ b.

Those two equations are easy to solve for a and b. Subtracting the first equation from the second, 82- 58= 24= (24- 17)a= 7a, eliminating b. a= 24/7. Notice that this gives exactly the equation for slope. Then 58= 17(24/7)+ b= 408/7+ b so b= 58- 408/7= 406/7- 408/7= -2/7. y= (24/7)x- 2/7.

For the second part, set x= 21 and evaluate.