Given that y 3 is in direct proportion to x, and x = 1, y = 5, translate the image of the function so that it passes (2, - 1), and find the analytic expression of the line after translation | Math enthusiast | Mathematical art

Given that y 3 is in direct proportion to x, and x = 1, y = 5, translate the image of the function so that it passes (2, - 1), and find the analytic expression of the line after translation

If "Y + 3 is in direct proportion to X",
Let y + 3 = KX and substitute x = 1 and y = 5,
The solution is k = 8,
∵ K remains unchanged in translation,
Let the analytic expression of the line after translation be y = 8x + B,
Substitute x = 2, y = - 1
The solution is b = - 17,
The analytic formula is y = 8x-17
If Y-3 is proportional to x,
Then k = 2,
Let y = 2x + B,
Substituting into the solution, we get b = - 5,
∴y=2x-5

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