Answer:
Step-by-step explanation:
Solve the given 3x + 5y = 2 for y. This will automatically indicate the slope of the line.
Subtracting 3x from both sides of this equation, we get:
5y = -3x = -3x + 2.
Dividing both sides by 5 yields y = (-3/5)x + 2/5.
The slope of the given line is -3/5. The y-intercept of this line is (0, 2/5).
Next time, please share the answer choicess. Thank you.
Answer:
Step-by-step explanation:
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We can model this situation with a linear equation. We know for our problem that the initial point is (0, 25), and the next point is (10, 108.4). To relate those points and find the slope of our linear equation, we are going to use the formula:
![m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} }](https://tex.z-dn.net/?f=m%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%20%7D%20)
. Notice that we know from our points that:
![x_{1}=0](https://tex.z-dn.net/?f=x_%7B1%7D%3D0)
,
![y_{1}=25](https://tex.z-dn.net/?f=y_%7B1%7D%3D25)
,
![x_{2}=10](https://tex.z-dn.net/?f=x_%7B2%7D%3D10)
, and
![y_{2}=108.4](https://tex.z-dn.net/?f=y_%7B2%7D%3D108.4)
. So, lets replace those values in our formula to find
![m](https://tex.z-dn.net/?f=m)
:
![m= \frac{108.4-25}{10-0}](https://tex.z-dn.net/?f=m%3D%20%5Cfrac%7B108.4-25%7D%7B10-0%7D%20)
![m= \frac{83.4}{10}](https://tex.z-dn.net/?f=m%3D%20%5Cfrac%7B83.4%7D%7B10%7D%20)
![m=8.34](https://tex.z-dn.net/?f=m%3D8.34)
Now that we have the slope of our linear equation, we can use the point slope formula:
![y-y_{1}=m(x-x_{1})](https://tex.z-dn.net/?f=y-y_%7B1%7D%3Dm%28x-x_%7B1%7D%29)
to complete our linear equation:
![y-25=8.34(x-0)](https://tex.z-dn.net/?f=y-25%3D8.34%28x-0%29)
![y-25=8.34x](https://tex.z-dn.net/?f=y-25%3D8.34x)
![y=8.34x+25](https://tex.z-dn.net/?f=y%3D8.34x%2B25)
Or in function notation:
![f(x)=8.34x+25](https://tex.z-dn.net/?f=f%28x%29%3D8.34x%2B25)
We can conclude that the equation that matches this situation is
![y=8.34x+25](https://tex.z-dn.net/?f=y%3D8.34x%2B25)
.