Question

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

hours miles from home
2 5.5
4 8.5
6 11.5
10 17.5
12 20.5
a. after 11 hours, johnny will be ___ miles from home.
b. at the beginning of the walk, johnny was ___ miles from home.
c. johnny was walking at a speed of ___ miles per hour.

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: Find the slope (speed)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((2,5.5)\) and \((4,8.5)\)
\(m=\frac{8.5 - 5.5}{4 - 2}=\frac{3}{2}=1.5\)

Step2: Find the y - intercept (initial distance)

Use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((2,5.5)\) and \(m = 1.5\)
\(y-5.5=1.5(x - 2)\)
\(y-5.5=1.5x-3\)
\(y=1.5x + 2.5\)

Answer:

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