A Line Has A Slope Of -5 And A $y$-intercept Of $\frac{4}{7}$. Write Its Equation In Slope-intercept Form.Write Your Answer Using Integers, Proper Fractions, And Improper Fractions In Simplest Form.
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Introduction
In mathematics, the slope-intercept form of a line is a fundamental concept that helps us understand the relationship between the slope and the y-intercept of a line. The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept. In this article, we will explore the concept of slope-intercept form and learn how to write the equation of a line with a given slope and y-intercept.
What is Slope-Intercept Form?
The slope-intercept form of a line is a way of expressing the equation of a line in terms of its slope and y-intercept. The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept. The slope (m) represents the rate of change of the line, while the y-intercept (b) represents the point where the line intersects the y-axis.
Understanding the Given Information
In this problem, we are given that the line has a slope of -5 and a y-intercept of . This means that the slope (m) is -5 and the y-intercept (b) is .
Writing the Equation in Slope-Intercept Form
To write the equation of the line in slope-intercept form, we need to substitute the given values of the slope and y-intercept into the equation y = mx + b. This gives us:
y = (-5)x +
Simplifying the Equation
To simplify the equation, we can multiply both sides of the equation by 7 to eliminate the fraction. This gives us:
7y = -35x + 4
Final Answer
The final answer is:
y = (-5)x +
Conclusion
In this article, we learned how to write the equation of a line in slope-intercept form given the slope and y-intercept. We also learned how to simplify the equation by eliminating fractions. The slope-intercept form is a powerful tool for understanding the relationship between the slope and y-intercept of a line.
Frequently Asked Questions
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
Q: How do I write the equation of a line in slope-intercept form?
A: To write the equation of a line in slope-intercept form, you need to substitute the given values of the slope and y-intercept into the equation y = mx + b.
Q: How do I simplify the equation of a line in slope-intercept form?
A: To simplify the equation of a line in slope-intercept form, you can multiply both sides of the equation by the denominator of the fraction to eliminate the fraction.
Additional Resources
Related Topics
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Introduction
In our previous article, we explored the concept of slope-intercept form and learned how to write the equation of a line with a given slope and y-intercept. In this article, we will answer some frequently asked questions about slope-intercept form and provide additional resources for further learning.
Q&A
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
Q: How do I write the equation of a line in slope-intercept form?
A: To write the equation of a line in slope-intercept form, you need to substitute the given values of the slope and y-intercept into the equation y = mx + b.
Q: How do I simplify the equation of a line in slope-intercept form?
A: To simplify the equation of a line in slope-intercept form, you can multiply both sides of the equation by the denominator of the fraction to eliminate the fraction.
Q: What is the difference between slope and y-intercept?
A: The slope (m) represents the rate of change of the line, while the y-intercept (b) represents the point where the line intersects the y-axis.
Q: How do I find the slope of a line?
A: To find the slope of a line, you can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Q: How do I find the y-intercept of a line?
A: To find the y-intercept of a line, you can use the equation y = mx + b and substitute the values of m and x into the equation to solve for b.
Q: Can I have a negative slope?
A: Yes, you can have a negative slope. A negative slope means that the line is decreasing as x increases.
Q: Can I have a zero slope?
A: Yes, you can have a zero slope. A zero slope means that the line is horizontal and does not change as x increases.
Q: Can I have a vertical line?
A: Yes, you can have a vertical line. A vertical line has an undefined slope and is represented by the equation x = a, where a is a constant.
Additional Resources
Related Topics
Conclusion
In this article, we answered some frequently asked questions about slope-intercept form and provided additional resources for further learning. We hope that this article has been helpful in understanding the concept of slope-intercept form and how to write the equation of a line with a given slope and y-intercept.
Frequently Asked Questions (FAQs)
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
Q: How do I write the equation of a line in slope-intercept form?
A: To write the equation of a line in slope-intercept form, you need to substitute the given values of the slope and y-intercept into the equation y = mx + b.
Q: How do I simplify the equation of a line in slope-intercept form?
A: To simplify the equation of a line in slope-intercept form, you can multiply both sides of the equation by the denominator of the fraction to eliminate the fraction.
Glossary
- Slope: The rate of change of the line.
- Y-intercept: The point where the line intersects the y-axis.
- Linear Equation: An equation that can be written in the form y = mx + b.
- Mathematics: The study of numbers, quantities, and shapes.