Problem

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Problem 77 Hard Difficulty

There is a linear relationship between a woman's height and the length of her radius bone. It can be stated this way:
Height increases by 3.9 inches for each 1-inch increase in the length of the radius. Suppose a 64 -inch-tall woman has a 9 -inch-long radius bone. Use this information to find a linear equation that relates height $h$ to the length $r$ of the radius. Write the equation in slope-intercept form.

Answer

$$h=3.9 r+28.9$$

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 3

Graphing Linear Equations and Inequalities in Two Variables; Functions

Section 6

Point–Slope Form

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Video Transcript

in this problem, we're told there's every a linear relationship between a woman's height in the length of her radius bone and the way they status, as they say that as height increases by 3.9 inch, it increases for every one inch increase in the radius full. Well, that's describing a rate of change will remember. The slope represents the rate of change in the problem. So in this particular case that telling us that the height is increasing 3.9 inches. So that's the changing the height for every one inch increase in the radius bone. So, in other words, to slope of this line would be 3.9 divided by one, which is 3.9. And that would be our rate of change, representing the change in the high for every inch increase in the radius boom. Now we're told the suppose of the woman who's 64 inches tall as a radius bone with a length of nine inches. What we want to do is use the information to find the linear equation that released the height to the length of the radius, so because they're giving us piece of information, that's essentially an ordered pair. Well, if you know this in when we found are so remember, Slope is a change in y over the change in acts. So our high is representing our why values and our ex is represented by the length of the radius bone. Therefore, the information that we get about the woman's height and length for a radius bone is going to be the order pair 9 64 Because remember, X is represented by the length of the radius foam and why is represented by the height? Well, now that we know the slope of the line and the point on the line now, we can use point slope form to write an equation for this line. Well, remember, point slope form is why minus weiss of one equals m times the quantity of X minus x of one. And don't forget em represents the slope. An ex of one and Weiss of one is a point on our line, which in this case, is our nine is going to your ex of one. And lice of one is going to be 64 now. The other thing to know in this problem is that they want us to use H and R Well, for this particular case, like we said, H is going to represent why and our is going to represent acts. So now we're gonna substitute all these values into our equation. Well, remember our why values are really r h values. So we're gonna have a beach minus Weiss of one, which is 64 equals R Slope, which is 3.9 times the quantity of X. But remember, exes really are in this case minus X of one, which is nine. Now we're being asked to put our final equation and slope intercept form, meaning we need to get the y value or sorry in this case to each value all by itself. So to do that, we first need to distribute 3.92 both terms in that Prem facie. So we'll be left with H minus 64 equals Well, 3.9 times are is just 3.9 are, and then we need to multiply 3.9 times negative nine, which is negative, 35 0.1. So now what I'm going to do is I'm gonna come over to the right side and rewrite this equation because I've kind of run out of room here. So we have each one of 64 equals 3.9 are minus 35.1. Remember, we're trying to get a GED by itself, which means we need to move that 64 to the other side. Well, to do that, we're gonna add 64 too. It's like term of negative 35.1. Now, though, 60 four's cancel out. So we're left with h equals 3.9 are just comes down. And negative. 35.1 plus 64 is positive. 28.9 and now with her in an equation in slope intercept form that released the height in the length of a radius bone.

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