Given The Equation 7 = X + 5 Y 7 = X + 5y 7 = X + 5 Y , Determine The Following:- Rate Of Change:- Slope:- Y-intercept:- X-intercept:

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Introduction

In this article, we will explore the concept of linear equations and how to determine various key components of a line given its equation. The equation $7 = x + 5y$ is a linear equation in two variables, x and y. To determine the rate of change, slope, y-intercept, and x-intercept of this line, we will use various mathematical techniques and formulas.

Rate of Change

The rate of change of a line is a measure of how much the output (y) changes when the input (x) changes by a certain amount. In other words, it measures the steepness of the line. To find the rate of change, we need to rewrite the equation in the slope-intercept form, which is $y = mx + b$, where m is the slope and b is the y-intercept.

To rewrite the equation, we need to isolate y on one side of the equation. We can do this by subtracting x from both sides of the equation and then dividing both sides by 5.

# Given equation: 7 = x + 5y
# Subtract x from both sides: 7 - x = 5y
# Divide both sides by 5: (7 - x) / 5 = y

Now that we have rewritten the equation in the slope-intercept form, we can see that the slope (m) is -1/5. This means that for every unit increase in x, y decreases by 1/5 units.

Slope

The slope of a line is a measure of how steep it is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run). In the case of the equation $7 = x + 5y$, the slope is -1/5.

# Slope (m) = -1/5

Y-intercept

The y-intercept of a line is the point where the line intersects the y-axis. It is the value of y when x is equal to 0. To find the y-intercept, we can substitute x = 0 into the equation and solve for y.

# Substitute x = 0 into the equation: 7 = 0 + 5y
# Solve for y: y = 7 / 5
# y-intercept = 7 / 5

X-intercept

The x-intercept of a line is the point where the line intersects the x-axis. It is the value of x when y is equal to 0. To find the x-intercept, we can substitute y = 0 into the equation and solve for x.

# Substitute y = 0 into the equation: 7 = x + 5(0)
# Solve for x: x = 7
# x-intercept = 7

Conclusion

In this article, we have determined the rate of change, slope, y-intercept, and x-intercept of the line given by the equation $7 = x + 5y$. We have used various mathematical techniques and formulas to find these key components of the line. The rate of change is -1/5, the slope is also -1/5, the y-intercept is 7/5, and the x-intercept is 7.

References

• [1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f8f7b
• [2] Math Open Reference. (n.d.). Linear Equations. Retrieved from https://www.mathopenref.com/linearequations.html

Discussion

• What is the rate of change of the line given by the equation $7 = x + 5y$?
• What is the slope of the line given by the equation $7 = x + 5y$?
• What is the y-intercept of the line given by the equation $7 = x + 5y$?
• What is the x-intercept of the line given by the equation $7 = x + 5y$?

Related Topics

• Linear Equations
• Slope-Intercept Form
• Rate of Change
• X-Intercept
• Y-Intercept
  

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Introduction

In our previous article, we explored the concept of linear equations and how to determine various key components of a line given its equation. The equation $7 = x + 5y$ is a linear equation in two variables, x and y. To determine the rate of change, slope, y-intercept, and x-intercept of this line, we used various mathematical techniques and formulas.

In this article, we will provide a Q&A section to help clarify any doubts or questions that readers may have. We will answer some of the most frequently asked questions related to the topic.

Q&A

Q1: What is the rate of change of the line given by the equation $7 = x + 5y$?

A1: The rate of change of the line given by the equation $7 = x + 5y$ is -1/5. This means that for every unit increase in x, y decreases by 1/5 units.

Q2: What is the slope of the line given by the equation $7 = x + 5y$?

A2: The slope of the line given by the equation $7 = x + 5y$ is also -1/5. This is because the slope is calculated as the ratio of the vertical change (rise) to the horizontal change (run).

Q3: What is the y-intercept of the line given by the equation $7 = x + 5y$?

A3: The y-intercept of the line given by the equation $7 = x + 5y$ is 7/5. This is the value of y when x is equal to 0.

Q4: What is the x-intercept of the line given by the equation $7 = x + 5y$?

A4: The x-intercept of the line given by the equation $7 = x + 5y$ is 7. This is the value of x when y is equal to 0.

Q5: How do I determine the rate of change, slope, y-intercept, and x-intercept of a line given its equation?

A5: To determine the rate of change, slope, y-intercept, and x-intercept of a line given its equation, you need to rewrite the equation in the slope-intercept form, which is $y = mx + b$, where m is the slope and b is the y-intercept. Then, you can use the formulas and techniques mentioned in our previous article to find the desired values.

Q6: What is the difference between the rate of change and the slope?

A6: The rate of change and the slope are related but distinct concepts. The rate of change measures how much the output (y) changes when the input (x) changes by a certain amount, while the slope measures the steepness of the line.

Q7: How do I find the x-intercept and y-intercept of a line given its equation?

A7: To find the x-intercept and y-intercept of a line given its equation, you need to substitute x = 0 into the equation and solve for y to find the y-intercept, and substitute y = 0 into the equation and solve for x to find the x-intercept.

Conclusion

In this article, we have provided a Q&A section to help clarify any doubts or questions that readers may have related to the topic of determining the rate of change, slope, y-intercept, and x-intercept of a line given its equation. We hope that this Q&A section has been helpful in providing a better understanding of the topic.

References

• [1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f8f7b
• [2] Math Open Reference. (n.d.). Linear Equations. Retrieved from https://www.mathopenref.com/linearequations.html

Discussion

• What is the rate of change of the line given by the equation $7 = x + 5y$?
• What is the slope of the line given by the equation $7 = x + 5y$?
• What is the y-intercept of the line given by the equation $7 = x + 5y$?
• What is the x-intercept of the line given by the equation $7 = x + 5y$?

Related Topics

• Linear Equations
• Slope-Intercept Form
• Rate of Change
• X-Intercept
• Y-Intercept