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Question is Incomplete; Complete question is given below.
Which expressions are equivalent to 8 (negative 10 x + 3.5 y minus 7)? Select two options. Negative 80 x + 24.5 y minus 56 Negative 80 x + 28 y minus 56 80 x + 28 y + 56 4 (negative 20 x + 7 y minus 14) Negative 4 (negative 20 x + 7 y minus 14)
Answer:
Negative 80 x + 28 y minus 56
4 (negative 20 x + 7 y minus 14)
Step-by-step explanation:
Given:
![8(-10x+3.5y-7)](https://tex.z-dn.net/?f=8%28-10x%2B3.5y-7%29)
We need to find the equivalent expression for given expression.
Solution:
![8(-10x+3.5y-7)](https://tex.z-dn.net/?f=8%28-10x%2B3.5y-7%29)
First we will apply distributive property for given expression.
![a(x+y) =ax+ay](https://tex.z-dn.net/?f=a%28x%2By%29%20%3Dax%2Bay)
So we get;
![8\times-10x+8\times3.5y-8\times7\\\\-80x+28y-56](https://tex.z-dn.net/?f=8%5Ctimes-10x%2B8%5Ctimes3.5y-8%5Ctimes7%5C%5C%5C%5C-80x%2B28y-56)
Hence first expression equivalent to given expression is
.
Now again evaluating the expression we get;
We will take 4 as common factor from the expression we get;
![-4\times20x+4\times7y-4\times14\\\\4(-20x+7y-14)](https://tex.z-dn.net/?f=-4%5Ctimes20x%2B4%5Ctimes7y-4%5Ctimes14%5C%5C%5C%5C4%28-20x%2B7y-14%29)
Hence second expression equivalent to given expression is
.
The equation of the line is
.
Solution:
The points on the line are (–6, –3) and (4, –5).
![x_{1}=-6, y_{1}=-3, x_{2}=4, y_{2}=-5](https://tex.z-dn.net/?f=x_%7B1%7D%3D-6%2C%20y_%7B1%7D%3D-3%2C%20x_%7B2%7D%3D4%2C%20y_%7B2%7D%3D-5)
Slope of the line:
![$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%24m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![$m=\frac{-5-(-3)}{4-(-6)}](https://tex.z-dn.net/?f=%24m%3D%5Cfrac%7B-5-%28-3%29%7D%7B4-%28-6%29%7D)
![$m=\frac{-5+3}{4+6}](https://tex.z-dn.net/?f=%24m%3D%5Cfrac%7B-5%2B3%7D%7B4%2B6%7D)
![$m=\frac{-2}{10}](https://tex.z-dn.net/?f=%24m%3D%5Cfrac%7B-2%7D%7B10%7D)
![$m=\frac{-1}{5}](https://tex.z-dn.net/?f=%24m%3D%5Cfrac%7B-1%7D%7B5%7D)
Point-slope formula:
![y-y_{1}=m\left(x-x_{1}\right)](https://tex.z-dn.net/?f=y-y_%7B1%7D%3Dm%5Cleft%28x-x_%7B1%7D%5Cright%29)
![$y-(-3)=\frac{-1}{5}(x-(-6))](https://tex.z-dn.net/?f=%24y-%28-3%29%3D%5Cfrac%7B-1%7D%7B5%7D%28x-%28-6%29%29)
![$y+3=\frac{-1}{5}(x+6)](https://tex.z-dn.net/?f=%24y%2B3%3D%5Cfrac%7B-1%7D%7B5%7D%28x%2B6%29)
![$y+3=\frac{-1}{5} x-\frac{6}{5}](https://tex.z-dn.net/?f=%24y%2B3%3D%5Cfrac%7B-1%7D%7B5%7D%20x-%5Cfrac%7B6%7D%7B5%7D)
Subtract 3 from both sides of the equation.
![$y=\frac{-1}{5} x-\frac{21}{5}](https://tex.z-dn.net/?f=%24y%3D%5Cfrac%7B-1%7D%7B5%7D%20x-%5Cfrac%7B21%7D%7B5%7D)
The equation of the line is
.
Answer: Yes, it can.
Step-by-step explanation: