Question

if L is a line whose equation is y= 3x +3 find the equation of the image of L under the translation (x,y) if x+4,y-4

Answer #1

The x intercept of the line ( when y = 0) is x = -1 and the y intercept (when x = 0) is y = 3.

So the line passes through the points (-1,0) and (0,3)

The y translation. y - 4, means that the line moves down by 4 units. Therefore the new y intercept = 3 - 4 = -1

The x translation. x + 4, means the line has moved 4 units to the left (+ means movemnet to the left), therefore the new x intercept = -1 - 4 = -5

The equation of the line given by the x intercept and the y intercept = (x/-5) + (y/-1) = 1

or -x/5 - y = 1

Therefore y = -x/5 - 1 (we can also write it as 5y = -x - 5 or x + 5y + 5 = 0)

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find the equation of the image of ℓ under each of the following
translations.
a. (x, y)right arrow→(x,yminus−44)
b.(x, y)→(x+2,y)
a. The equation of the image of ℓ under the
translation (x, y)→(x, y-4) is?????

If 5x^2+3x+xy=3 and y(3)=-17, find y'(3) by implicit
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Thus an equation of the tangent line to the graph at the point
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b. y = -1/3 - 2
c. y = 3x + 26
d. y = 3x + 24

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(2 + 3x)^2 y'' − 3(2 + 3x)y' + 9y = 81x x > −
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y=4x. Give an exact answer

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