A Line Passes Through The Points { (-4, -8)$}$ And { (-2, -4)$}$. Write Its Equation In Slope-intercept Form.Write Your Answer Using Integers, Proper Fractions, And Improper Fractions In Simplest Form. { \square$}$
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. Given two points on a line, we can find the equation of the line in slope-intercept form using the slope formula and the point-slope form of a line. In this article, we will explore how to find the equation of a line passing through two points, and , in slope-intercept form.
The Slope Formula
The slope formula is a fundamental concept in mathematics that helps us find the slope of a line passing through two points. The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
where m is the slope of the line, and (x1, y1) and (x2, y2) are the coordinates of the two points.
Finding the Slope
To find the slope of the line passing through the points and , we can use the slope formula:
m = (-4 - (-8)) / (-2 - (-4))
m = (4) / (2)
m = 2
Therefore, the slope of the line passing through the points and is 2.
The Point-Slope Form of a Line
The point-slope form of a line is a fundamental concept in mathematics that helps us find the equation of a line passing through a point and having a given slope. The point-slope form of a line is given by:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is the point on the line.
Finding the Equation of the Line
To find the equation of the line passing through the points and , we can use the point-slope form of a line:
y - (-8) = 2(x - (-4))
y + 8 = 2(x + 4)
y + 8 = 2x + 8
y = 2x
Therefore, the equation of the line passing through the points and in slope-intercept form is y = 2x.
Conclusion
In this article, we explored how to find the equation of a line passing through two points, and , in slope-intercept form. We used the slope formula and the point-slope form of a line to find the equation of the line. The equation of the line passing through the points and in slope-intercept form is y = 2x.
References
- [1] "Slope-Intercept Form of a Line." Math Open Reference, mathopenref.com/slope-intercept.html.
- [2] "Point-Slope Form of a Line." Math Open Reference, mathopenref.com/point-slope-form.html.
Additional Resources
- [1] Khan Academy. "Slope-Intercept Form of a Line." Khan Academy, khanacademy.org/math/algebra/linear-equations-and-functions/slope-intercept-form-of-a-line/v/slope-intercept-form-of-a-line.
- [2] Mathway. "Slope-Intercept Form of a Line." Mathway, mathway.com/subject/math/algebra/slope-intercept-form-of-a-line.
A Line Passing Through Two Points: Finding the Equation in Slope-Intercept Form - Q&A ====================================================================================
Introduction
In our previous article, we explored how to find the equation of a line passing through two points, and , in slope-intercept form. We used the slope formula and the point-slope form of a line to find the equation of the line. In this article, we will answer some frequently asked questions related to finding the equation of a line passing through two points in slope-intercept form.
Q: What is the slope-intercept form of a line?
A: The slope-intercept form of a line is a mathematical equation that represents a line in the form y = mx + b, where m is the slope of the line and b is the y-intercept of the line.
Q: How do I find the slope of a line passing through two points?
A: To find the slope of a line passing through two points, you can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where m is the slope of the line, and (x1, y1) and (x2, y2) are the coordinates of the two points.
Q: What is the point-slope form of a line?
A: The point-slope form of a line is a mathematical equation that represents a line in the form y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point on the line.
Q: How do I find the equation of a line passing through two points in slope-intercept form?
A: To find the equation of a line passing through two points in slope-intercept form, you can use the point-slope form of a line and then simplify the equation to the slope-intercept form.
Q: What if the slope of the line is zero?
A: If the slope of the line is zero, then the equation of the line is in the form y = b, where b is the y-intercept of the line.
Q: What if the slope of the line is undefined?
A: If the slope of the line is undefined, then the line is a vertical line and the equation of the line is in the form x = a, where a is the x-coordinate of the line.
Q: Can I use the slope-intercept form to find the equation of a line passing through three points?
A: No, the slope-intercept form is used to find the equation of a line passing through two points. If you have three points, you can use the point-slope form to find the equation of the line.
Q: How do I graph a line passing through two points in slope-intercept form?
A: To graph a line passing through two points in slope-intercept form, you can use the slope-intercept form to find the y-intercept of the line and then use the slope to find the x-intercept of the line.
Conclusion
In this article, we answered some frequently asked questions related to finding the equation of a line passing through two points in slope-intercept form. We hope that this article has been helpful in understanding the concept of finding the equation of a line passing through two points in slope-intercept form.
References
- [1] "Slope-Intercept Form of a Line." Math Open Reference, mathopenref.com/slope-intercept.html.
- [2] "Point-Slope Form of a Line." Math Open Reference, mathopenref.com/point-slope-form.html.
Additional Resources
- [1] Khan Academy. "Slope-Intercept Form of a Line." Khan Academy, khanacademy.org/math/algebra/linear-equations-and-functions/slope-intercept-form-of-a-line/v/slope-intercept-form-of-a-line.
- [2] Mathway. "Slope-Intercept Form of a Line." Mathway, mathway.com/subject/math/algebra/slope-intercept-form-of-a-line.