8,-4);3x-5y=8 slope parallel ?
1 answer:
Let us first bring the equation given into the slope-intercept form.
We see that the above equation has slope 3/ 5, and therefore, the equation that we want to construct must also have this slope. Hence, we already know that the equation we are seeking must take the form
where b is the y-intercept yet unknown.
Let us plug in (x, y) = (8, -4) in the above equation, this gives
Hence, the equation of the line in slope-intercept form is
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Answer:
y = x⁴ + x³ - 3x² + 5x + C
======
Separable differential equations such as these ones can be solved by treating dy/dx as a ratio of differentials. Then move the dx with all the x terms and move the dy with all the y terms. After that, integrate both sides of the equation.
In general (understood that +C portions are still there),
Note that ∫dy = y since it is ∫1·dy = ∫y⁰ dy = y¹/(0+1) = y
For the right-hand side, we use the sum/difference rule for integrals, which says that
![\int \big[f(x) \pm g(x)\big]\, dx = \int f(x)\,dx \pm \int g(x) \, dx](https://tex.z-dn.net/?f=%5Cint%20%5Cbig%5Bf%28x%29%20%5Cpm%20g%28x%29%5Cbig%5D%5C%2C%20dx%20%3D%20%5Cint%20f%28x%29%5C%2Cdx%20%5Cpm%20%5Cint%20g%28x%29%20%5C%2C%20dx)
Applying these concepts:
The answer is y = x⁴ + x³ - 3x² + 5x + C
y = x⁴ + x³ - 3x² + 5x + C
======
Separable differential equations such as these ones can be solved by treating dy/dx as a ratio of differentials. Then move the dx with all the x terms and move the dy with all the y terms. After that, integrate both sides of the equation.
In general (understood that +C portions are still there),
Note that ∫dy = y since it is ∫1·dy = ∫y⁰ dy = y¹/(0+1) = y
For the right-hand side, we use the sum/difference rule for integrals, which says that
Applying these concepts:
The answer is y = x⁴ + x³ - 3x² + 5x + C