-(9-1)-point-slope-form.jpeg "(-6 6) (9 1) Point Slope Form")
Point-Slope Form: Understanding the Concept
Point-slope form is a way to express the equation of a line in mathematics. It is one of the three primary forms of linear equations, alongside slope-intercept form and standard form. In this article, we will delve into the world of point-slope form, using the example of (-6, 6) and (9, 1) to illustrate the concept.
What is Point-Slope Form?
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where:
- (x1, y1) is a point on the line
- m is the slope of the line
This form is useful when we know the slope of the line and a point on the line. By plugging in the values of m, x1, and y1, we can find the equation of the line.
Example: (-6, 6) and (9, 1)
Let's say we have two points, (-6, 6) and (9, 1). We can use these points to find the equation of the line in point-slope form.
First, we need to find the slope (m) of the line. To do this, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-6, 6) and (x2, y2) = (9, 1).
m = (1 - 6) / (9 - (-6)) m = (-5) / 15 m = -1/3
Now that we have the slope, we can use either point to find the equation of the line in point-slope form. Let's use the point (-6, 6).
y - 6 = (-1/3)(x - (-6))
Simplifying the equation, we get:
y - 6 = (-1/3)(x + 6) y - 6 = (-1/3)x - 2 y = (-1/3)x + 4
And that's it! We have found the equation of the line in point-slope form using the points (-6, 6) and (9, 1).
Importance of Point-Slope Form
Point-slope form is a powerful tool in mathematics, particularly in algebra and geometry. It allows us to:
- Find the equation of a line given a point and the slope
- Identify parallel and perpendicular lines
- Solve systems of linear equations
In conclusion, point-slope form is an essential concept in mathematics that can help us solve a wide range of problems. By mastering this concept, we can unlock the secrets of linear equations and take our problem-solving skills to the next level.
