Question

going for a walk
story
miss johnson walks at a rate of 2 miles per hour.
x = hour
y = miles walked
table
(chart with x values 0,1,2,3,4 and empty y column)
graph
walking miles (y - axis: 0 - 10, x - axis: 0 - 7 hours)
constant of proportionality
equation
write your own question & answer

Explanation:

To solve the problem of filling the table for Miss Johnson's walk, we use the relationship between time (\(x\)) and distance (\(y\)) given by her walking rate.

Step 1: Understand the Relationship

Miss Johnson walks at a rate of 2 miles per hour. The distance \(y\) (in miles) she walks in \(x\) hours is given by the formula:
\( y = 2x \)

Step 2: Calculate \(y\) for \(x = 0\)

Substitute \(x = 0\) into the formula:
\( y = 2(0) = 0 \)

Step 3: Calculate \(y\) for \(x = 1\)

Substitute \(x = 1\) into the formula:
\( y = 2(1) = 2 \)

Step 4: Calculate \(y\) for \(x = 2\)

Substitute \(x = 2\) into the formula:
\( y = 2(2) = 4 \)

Step 5: Calculate \(y\) for \(x = 3\)

Substitute \(x = 3\) into the formula:
\( y = 2(3) = 6 \)

Step 6: Calculate \(y\) for \(x = 4\)

Substitute \(x = 4\) into the formula:
\( y = 2(4) = 8 \)

Filled Table

\(x\) (hours)	\(y\) (miles)
1	2
2	4
3	6
4	8

Constant of Proportionality

The relationship \( y = 2x \) is proportional, so the constant of proportionality (the rate) is \( 2 \).

Equation

The equation relating \(x\) (hours) and \(y\) (miles) is:
\( y = 2x \)

Write Your Own Question & Answer

Question: How many miles does Miss Johnson walk in 5 hours?

Answer:

** Substitute \(x = 5\) into \( y = 2x \):
\( y = 2(5) = 10 \)
She walks 10 miles in 5 hours.

Graphing

To plot the points on the graph:

• For \(x = 0\), \(y = 0\) (point: \((0, 0)\))
• For \(x = 1\), \(y = 2\) (point: \((1, 2)\))
• For \(x = 2\), \(y = 4\) (point: \((2, 4)\))
• For \(x = 3\), \(y = 6\) (point: \((3, 6)\))
• For \(x = 4\), \(y = 8\) (point: \((4, 8)\))

Plot these points on the graph (with \(x\) as "Hours" and \(y\) as "Miles Walked") and draw a straight line through them.