High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
15th Edition
ISBN: 9780133281149
Author: Prentice Hall
Publisher: Prentice Hall
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Question
Chapter 5.6, Problem 26PPE
To determine
To frame: an equation of a bike path which is parallel to the given main street and passing through park entrance.
Expert Solution & Answer
Answer to Problem 26PPE
The required equation of bike path is, y = 2x + 4
Explanation of Solution
Given Information
The given graph represents a main street and a bike path needs to be constructed, which will be parallel to the main street.
So, firstly, we will have to find out the equation of the main street from the given graph.
Then, we will set up an equation, parallel to the main street and passing through the co-ordinates of the park entrance.
Formula Used
y = mx + C
Where, ‘ x’ and ‘ y’ are variables and ‘ m’ is the slope of the equation, ‘ c’ being the y intercept respectively.
And Slope =
Graphical Approach
Calculation
Finding equation of main street:
It passes through,
So, y -intercept = −3
Slope =
So, Slope = m = 2
Equation of main street ⇒ y = mx + C
⇒y = 2x − 3
Now, the equation of bike path will be parallel to main street,
So, slope of bike path will also be, m = 2
Conclusion
Now, we are required to frame the equation of bike path
Hence, equation of bike path,
y = mx + C ; where m = 2
⇒y = 2x + C
But we know this line will pass through park entrance (0, 4)
Putting, (0, 4) in y = 2x + C
we get ⇒ 4 = 2 × 0 + C ( C = 4
Therefore, the required equation of bike path is, y = 2x + 4
Chapter 5 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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