Lesson 18
Two Related Quantities, Part 2
Let’s use equations and graphs to describe stories with constant speed.
Problem 1
A car is traveling down a road at a constant speed of 50 miles per hour.
- Complete the table with the amounts of time it takes the car to travel certain distances, or the distances traveled for certain amounts of time.
-
Write an equation that represents the distance traveled by the car, \(d\), for an amount of time, \(t\).
- In your equation, which is the dependent variable and which is the independent variable?
time (hours) | distance (miles) |
---|---|
2 | |
1.5 | |
\(t\) | |
50 | |
300 | |
\(d\) |
Problem 2
The graph represents the amount of time in hours it takes a ship to travel various distances in miles.
![A graph of 10 points plotted on the coordinate plane.](https://cms-im.s3.amazonaws.com/5PujLPLrHtTZfZkAz84CULzo?response-content-disposition=inline%3B%20filename%3D%226-6.6.D1.Image.45.png%22%3B%20filename%2A%3DUTF-8%27%276-6.6.D1.Image.45.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182407Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=cb7b6fb9ecc85a88884fdfe9b17de59a2ef641134807497a5ddecfea6bbacac2)
- Write the coordinates of one point on the graph. What does the point represent?
- What is the speed of the ship in miles per hour?
- Write an equation that relates the time, \(t\), it takes to travel a given distance, \(d\).
Problem 3
Find a solution to each equation in the list that follows (not all numbers will be used):
-
\(2^x=8\)
-
\(2^x=2\)
-
\(x^2=100\)
-
\(x^2=\frac{1}{100}\)
-
\(x^1=7\)
-
\(2^x\boldcdot 2^3=2^7\)
-
\(\frac{2^x}{2^3}=2^5\)
List:
\(\frac{1}{10}\)
\(\frac{1}{3}\)
1
2
3
4
5
7
8
10
16
Problem 4
Select all the expressions that are equivalent to \(5x +30x - 15x\).
\(5(x + 6x-3x)\)
\((5+30-15)\boldcdot x\)
\(x(5+30x-15x)\)
\(5x(1+6-3)\)
\(5(x+30x-15x)\)
Problem 5
Evaluate each expression if \(x\) is 1, \(y\) is 2, and \(z\) is 3.
- \(7x^2-z\)
- \((x+4)^3-y\)
- \(y(x + 3^3)\)
- \((7-y+z)^2\)
- \(0.241x + x^3\)