Four-legged animals run with two different types of motion: trotting and galloping. An animal that is trotting has at least one foot on the ground at all times, whereas an animal that is galloping has all four feet off the ground at some point in its stride. The number of strides per minute at which an animal breaks from a trot to a gallop depends on the weight of the animal.
1. Use the table and the method of this example to find an equation that relates an animal's weight x (in pounds) and its lowest galloping speed y (in strides per minute).
weight, X 25 35 50 75 500 1000
Galloping speed, Y 191.5 184.7 175.8 162.2 124.9 113.2

Galloping speed Y=179.984-0.076 weight X

Step-by-step explanation:

The required equation is

y=a+bx

where y is galloping speed and x is weight of animal.

We have to estimate intercept a and slope b.

x                  y        xy      x²

25    191.54787.5625

35    184.76464.51225

50    175.887902500

75    162.2121655625

500  124.962450250000

1000113.21132001000000

sumx=1685

sumy=952.3

sumxy=207857

sumx²=1259975

slope=b=-0.07573.

intercept=a=ybar-b*xbar

ybar=158.7167

xbar=280.8333

intercept=a=ybar-b*xbar

intercept=a=158.7167-(-0.07573)*280.8333

intercept=a=158.7167+21.2675

intercept=a=179.9842

rounding intercept and slope to 3 decimal places

intercept=179.984.

slope=-0.076

The required equation is

Galloping speed Y=179.984-0.076 weight X

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

the correct answer is d

hope this