Question

1. johnny is walking at a uniform speed. the table shows his distance from home when started walking. (note: he did not start from home.)

1. which equation represents the correct equation for the table in question #6?

a. ( y = 2.5x + 1.5 )
b. ( y = 3x + 5.5 )
c. ( y = 20.5x + 12 )
d. ( y = 1.5x + 2.5 )
e. ( y = 5.5x + 2 )

1. for which of the following can the dependent variable and independent variable be reversed.

a. as the amount of daily sugar increases, the risk for diabetes increases.
b. as the number of factories increases, the amount of pollution increases.
c. as the amount of flour used increases, the thickness of gravy increases.
d. as the age of an infant increases, the weight of the infant increases.
e. as the number of lights turned on increases, the electrical bill increases.

Explanation:

Step1: Identify the linear equation form

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope (speed in this context) and \(b\) is the \(y\)-intercept (initial distance from home). From question 6c, \(m = 1.5\) (speed), and from 6b, \(b=2.5\) (initial distance).

Step2: Check the equation

Substitute \(m = 1.5\) and \(b = 2.5\) into \(y=mx + b\). We get \(y = 1.5x+2.5\).

Answer:

d. \(y = 1.5x + 2.5\)