Answer:
Slope = -1
Step-by-step explanation:
Use the following formula:
slope (m) = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (1 , -3)
(x₂ , y₂) = (3 , -5)
Plug in the corresponding numbers to the corresponding variables. Simplify:
m = (-5 - (-3))/(3 - 1)
m = (-5 + 3)/(3 - 1)
m = -2/2
m = -1
The slope of the line is -1.
~
Add 121 to 245 to get your answer.
the unit rate is 121, so you add 121 everytime
Answer:
Area = ![f(x)=10x^2 + 31x + 15](https://tex.z-dn.net/?f=f%28x%29%3D10x%5E2%20%2B%2031x%20%2B%2015)
Step-by-step explanation:
The function is the area function of a rectangle.
Area of Rectangle = Length * Width
Length of fabric scrap = 5x
Length of rectangular patchwork will be 5x + 3
and
Width of fabric scrap = 2x
Width of rectangular patchwork will be 2x + 5
THus, Area = (5x+3)(2x+5) square feet.
Let's expand:
![Area = f(x) = (5x+3)(2x+5)\\f(x)=10x^2 + 25x + 6x + 15\\f(x)=10x^2 + 31x + 15](https://tex.z-dn.net/?f=Area%20%3D%20f%28x%29%20%3D%20%285x%2B3%29%282x%2B5%29%5C%5Cf%28x%29%3D10x%5E2%20%2B%2025x%20%2B%206x%20%2B%2015%5C%5Cf%28x%29%3D10x%5E2%20%2B%2031x%20%2B%2015)
The value of
and ![b = 5](https://tex.z-dn.net/?f=b%20%3D%205)
<u>Solution:</u>
Given, Line passes through points ![A(-6,6) = (x_1, y_1); \ B(12,3) = (x_2 , y_2)](https://tex.z-dn.net/?f=A%28-6%2C6%29%20%3D%20%28x_1%2C%20y_1%29%3B%20%5C%20B%2812%2C3%29%20%3D%20%28x_2%20%2C%20y_2%29)
Slope of line passing through two points is ![m = \frac{(y_2-y_1)}{(x_2-x_1)}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B%28y_2-y_1%29%7D%7B%28x_2-x_1%29%7D)
![\rightarrow \frac{(3-6)}{(12- (-6))}](https://tex.z-dn.net/?f=%5Crightarrow%20%5Cfrac%7B%283-6%29%7D%7B%2812-%20%28-6%29%29%7D)
![\rightarrow \frac{-3}{18} = \frac{-1}{6}](https://tex.z-dn.net/?f=%5Crightarrow%20%5Cfrac%7B-3%7D%7B18%7D%20%3D%20%5Cfrac%7B-1%7D%7B6%7D)
Equation of a straight line passing through point-slope form is ![y - y1 = m (x - x1) --- (1)](https://tex.z-dn.net/?f=y%20-%20y1%20%3D%20m%20%28x%20-%20x1%29%20---%20%281%29)
Since we have two points we can use any point. Let us take
and m
and substitute in (1)
![\Rightarrow y - 6 = \frac{-1}{6 (x - (-6))}](https://tex.z-dn.net/?f=%5CRightarrow%20y%20-%206%20%3D%20%5Cfrac%7B-1%7D%7B6%20%28x%20-%20%28-6%29%29%7D)
![\Rightarrow y - 6 = \frac{-1}{6x -1}](https://tex.z-dn.net/?f=%5CRightarrow%20y%20-%206%20%3D%20%5Cfrac%7B-1%7D%7B6x%20-1%7D)
[By equating as
]
![m = \frac{-1}{6} ; b = 5](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1%7D%7B6%7D%20%3B%20b%20%3D%205)
Substituting the other coordinates also gives the same result.
Answer:
The value of k is -5.
Step-by-step explanation:
To find the value of k, start by using the known information we have in the equation for slope. The equation is below.
m(slope) = (y2 - y1)/(x2 - x1)
In this equation, the first ordered pair would be (x1, y1) and the second would be (x2 , y2). So we put the values in for these variables and we get.
-1/5 = (-7 - k)/(6 + 4)
-1/5 = (-7 - k)/10
Now we can use cross multiplication to solve for k.
-1/5 = (-7 - k)/10
-1*10 = 5(-7 - k)
-10 = -35 - 5k
25 = -5k
-5 = k