Find The Equation Of The Line Specified. The Slope Is \[$-7\$\], And It Passes Through \[$(5, -3)\$\].A. \[$y = -7x - 3\$\] B. \[$y = -7x + 32\$\] C. \[$y = -14x + 32\$\] D. \[$y = -7x - 38\$\]Please
=====================================================
Introduction
In mathematics, the equation of a line can be determined using the slope-intercept form, which is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. In this article, we will discuss how to find the equation of a line given its slope and a point it passes through.
The Slope-Intercept Form
The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line is a measure of how steep it is, and it is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
Finding the Equation of a Line
To find the equation of a line given its slope and a point it passes through, we can use the point-slope form of a line, which is given by the equation y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.
Example
Given the slope m = -7 and the point (5, -3), we can use the point-slope form to find the equation of the line.
Step 1: Write Down the Point-Slope Form
The point-slope form of a line is given by the equation y - y1 = m(x - x1). In this case, we have m = -7 and the point (5, -3).
Step 2: Plug in the Values
We can plug in the values of m and the point (5, -3) into the point-slope form to get:
y - (-3) = -7(x - 5)
Step 3: Simplify the Equation
We can simplify the equation by combining like terms:
y + 3 = -7x + 35
Step 4: Write the Equation in Slope-Intercept Form
We can write the equation in slope-intercept form by isolating y:
y = -7x + 32
Conclusion
In this article, we discussed how to find the equation of a line given its slope and a point it passes through. We used the point-slope form of a line and simplified the equation to find the slope-intercept form. The equation of the line is y = -7x + 32.
Comparison with Answer Choices
We can compare our answer with the answer choices to see which one matches:
- A. y = -7x - 3
- B. y = -7x + 32
- C. y = -14x + 32
- D. y = -7x - 38
Our answer matches answer choice B.
Final Answer
The final answer is B. y = -7x + 32.
=====================================================
Introduction
In our previous article, we discussed how to find the equation of a line given its slope and a point it passes through. In this article, we will provide a Q&A section to help you better understand the concept and to address any questions you may have.
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 of the line and b is the y-intercept.
Q: How do I find the slope of a line?
A: The slope of a line can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Q: What is the point-slope form of a line?
A: The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Q: How do I use the point-slope form to find the equation of a line?
A: To use the point-slope form to find the equation of a line, you can plug in the values of m and the point (x1, y1) into the equation y - y1 = m(x - x1). Then, simplify the equation to find the slope-intercept form.
Q: What if I have a horizontal line? How do I find its equation?
A: If you have a horizontal line, its equation will be in the form y = b, where b is the y-intercept. To find the equation of a horizontal line, you can use the point-slope form and set the slope (m) to 0.
Q: What if I have a vertical line? How do I find its equation?
A: If you have a vertical line, its equation will be in the form x = a, where a is the x-intercept. To find the equation of a vertical line, you can use the point-slope form and set the slope (m) to infinity.
Q: Can I use the point-slope form to find the equation of a line if I have two points?
A: Yes, you can use the point-slope form to find the equation of a line if you have two points. However, you will need to find the slope (m) first using the formula m = (y2 - y1) / (x2 - x1).
Q: What if I have a line with a negative slope? How do I find its equation?
A: If you have a line with a negative slope, you can use the point-slope form and plug in the values of m and the point (x1, y1) into the equation y - y1 = m(x - x1). Then, simplify the equation to find the slope-intercept form.
Q: Can I use the point-slope form to find the equation of a line if I have a point and the slope is not given?
A: Yes, you can use the point-slope form to find the equation of a line if you have a point and the slope is not given. However, you will need to find the slope (m) first using the formula m = (y2 - y1) / (x2 - x1).
Conclusion
In this article, we provided a Q&A section to help you better understand the concept of finding the equation of a line given its slope and a point it passes through. We hope this article has been helpful in addressing any questions you may have had.
Final Tips
- Make sure to use the point-slope form to find the equation of a line.
- Simplify the equation to find the slope-intercept form.
- Use the formula m = (y2 - y1) / (x2 - x1) to find the slope of a line.
- Use the point-slope form to find the equation of a line if you have two points.
- Use the point-slope form to find the equation of a line if you have a point and the slope is not given.
Final Answer
The final answer is B. y = -7x + 32.