Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 8: Problem 58
Graph. \(2(y-7)=y-10\)
Short Answer
Expert verified
y = 4
Step by step solution
01
Distribute 2 on the left side of the equation
Distribute the multiplication on the left side to get rid of the parenthesis: 2(y-7) = 2y - 14
02
Write the equation
Rewrite the equation with the distributed form: 2y - 14 = y - 10
03
Move all y terms to one side
Subtract y from both sides: 2y - 14 - y = y - y - 10 This simplifies to: y - 14 = -10
04
Add 14 to both sides
To isolate y, add 14 to both sides of the equation: y - 14 + 14 = -10 + 14 This simplifies to: y = 4
05
Conclusion
The solution to the equation is y = 4.
06
Graph the solution
Since y is a constant value 4, it is independent of x. The graph will be a horizontal line that intersects the y-axis at y = 4.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with 91影视!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Equation Distribution
Understanding **equation distribution** is essential when solving linear equations. This process involves distributing a multiplier across terms within parentheses. Consider the example provided:
\(2(y-7)=y-10\).
In step 1, we distribute the 2 across each term inside the parentheses:
\(2(y-7) = 2 \times y - 2 \times 7\), which simplifies to \(2y - 14\).
By distributing, we have removed the parentheses, making the equation easier to solve.
\(2(y-7)=y-10\).
In step 1, we distribute the 2 across each term inside the parentheses:
\(2(y-7) = 2 \times y - 2 \times 7\), which simplifies to \(2y - 14\).
By distributing, we have removed the parentheses, making the equation easier to solve.
- Always distribute multiplication over addition or subtraction inside parentheses.
- This step helps simplify the equation, allowing you to combine like terms.
Isolating Variables
After distributing, the next critical step is **isolating variables**. The goal is to get the variable alone on one side of the equation. Here鈥檚 how it's done in our example:
1. With the distributed form, rewrite the equation: \(2y - 14 = y - 10\).
2. Move all y terms to one side by subtracting y from both sides: \(2y - 14 - y = y - y - 10\). This simplifies to \(y - 14 = -10\).
3. Isolate y by adding 14 to both sides: \(y - 14 + 14 = -10 + 14\), which simplifies to \(y = 4\).
1. With the distributed form, rewrite the equation: \(2y - 14 = y - 10\).
2. Move all y terms to one side by subtracting y from both sides: \(2y - 14 - y = y - y - 10\). This simplifies to \(y - 14 = -10\).
3. Isolate y by adding 14 to both sides: \(y - 14 + 14 = -10 + 14\), which simplifies to \(y = 4\).
- Remember, always perform the same operation on both sides of the equation to maintain balance.
- This isolates the variable, allowing you to find its value.
Graphing Solutions
Once you find the solution to the equation, the next step is **graphing** it. The solution \(y = 4\) tells us that y is always 4, no matter the value of x. Since the solution is independent of x, the graph will be a horizontal line.
Understanding how to graph solutions helps visualize equations and their solutions, providing a clearer insight into the relationship between variables.
- To graph the line, simply draw a horizontal line that intersects the y-axis at y = 4.
- Every point on this line has a y-coordinate of 4, which illustrates the solution to the equation.
Understanding how to graph solutions helps visualize equations and their solutions, providing a clearer insight into the relationship between variables.
Horizontal Line Graph
A **horizontal line graph** is a particular type of graph that represents a constant y-value across all x-values. In the case of our example equation, the result is \(y = 4\). This can be interpreted as:
Horizontal lines are easy to recognize on a graph as they indicate that one variable remains unchanged. Understanding this concept is fundamental when dealing with equations that result in constants for one of the variables.
- No matter what value x takes, y will always be 4.
- This relationship is shown as a horizontal line at y = 4 on the Cartesian plane.
Horizontal lines are easy to recognize on a graph as they indicate that one variable remains unchanged. Understanding this concept is fundamental when dealing with equations that result in constants for one of the variables.
