First, let's find the slope of the line using the slope formula, which is:
![m = \dfrac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
((
,
) and (
,
) are points on the line)
In context of this problem, we can use the formula to find the slope of the line between the two points:
![m = \dfrac{-2 -6}{7 - (-1)} = \dfrac{-8}{8} = -1](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7B-2%20-6%7D%7B7%20-%20%28-1%29%7D%20%3D%20%5Cdfrac%7B-8%7D%7B8%7D%20%3D%20-1)
Now, we can use the slope in the point-slope formula, which will help us find the final equation of the line. (For reference, the point-slope formula is
where (
,
) is a point on the line)
In the context of the problem, we could use the formula to find the equation of the line:
![(y - 6) = -1(x + 1)](https://tex.z-dn.net/?f=%28y%20-%206%29%20%3D%20-1%28x%20%2B%201%29)
![(y - 6) = -x - 1](https://tex.z-dn.net/?f=%28y%20-%206%29%20%3D%20-x%20-%201)
![\boxed{y = -x + 5}](https://tex.z-dn.net/?f=%5Cboxed%7By%20%3D%20-x%20%2B%205%7D)
The equation of the line is y = -x + 5.
Answer:
53! I think hope this helped☺️
-by-step explanation:
1) slope is (8-1)/(4-(-6))=7/10
2) slope is (3-5.2)/(3.25-(-42.25))=-2.2/45.50=-22/455
3) the slope of 1 means the line is inclined to the horizontal axis at an angle of 45 degrees. There are an infinite number of such parallel lines, but only one y=x passes through the origin.
<h2>
The all roots are equation are 1, - 1 and - 2.</h2>
Step-by-step explanation:
The given cubic polynomial:
k(x) =
+ 2
- x -2
To find, the all roots are
+ 2
- x -2 = ?
∴ k(x) =
+ 2
- x -2
⇒
+ 2
- x -2 = 0
⇒
(x + 2) - 1(x + 2) = 0
⇒ (
- 1)(x + 2) = 0
⇒
- 1 = 0 and x + 2 = 0
⇒
- 1 = 0
⇒
= 1
⇒ x = ± 1 = 1, - 1
or, x + 2 = 0
⇒ x = - 2
Thus, the all roots are equation are 1, - 1 and - 2.