Question

Bob drew a line he thought was close to many of the points and found the equation of the line. He used the points (165, 168) and (174, 178) on his line to find the equation. What is the equation of Bob’s line? If entering decimal values, round to the tenths place.
What does Bob’s equation predict for the height of a person with an arm span of 162 cm? If entering a decimal value, round to the tenths place

Answer 1

We will see that the linear equation is:

y = 1.1*x  -13.5

b) The predicted height is 164.7cm

How to get the linear equation?

A general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ - x₁)

In this case, the line passes through (165, 168) and (174, 178), then the slope is:

a = (178 - 168)/(174 - 165) = 10/9 = 1.1

Then the line is:

y = 1.1*x + b

To get the value of b, we use one of the given points, for example if we use the first one (165, 168) we must have x = 165 and y = 168, replacing that we get:

168 = 1.1*165 + b

168 -  1.1*165  = b = -13.5

The equation is:

y = 1.1*x  -13.5

Now we want to find the height of a person with an arm span of 162cm, then we replace x by 162 to get:

y = 1.1*162 -13.5 = 164.7

The predicted height is 164.7cm

If you want to learn more about linear equations, you can read:

brainly.com/question/1884491