Question

if L is a line whose equation is y= 3x +3 find the equation of the...

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

Homework Answers

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)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
If ℓ is a line whose equation is y=7x−2​, find the equation of the image of...
If ℓ is a line whose equation is y=7x−2​, 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 differentiation. Thus an equation of the tangent line...
If 5x^2+3x+xy=3 and y(3)=-17, find y'(3) by implicit differentiation. Thus an equation of the tangent line to the graph at the point (3,-17) is
Find the point on the line 3x + y = 7 that is closest to the...
Find the point on the line 3x + y = 7 that is closest to the point (−4, 3) (x,y) =
find the equation of a tangent line(s) to the curve with slope 5 f(x)=x^3 + 3x^2...
find the equation of a tangent line(s) to the curve with slope 5 f(x)=x^3 + 3x^2 - 4x - 12 f'(x)= 3x^2 +6x - 4
find the equation of the tangent line to the curve y=e^-3x • cosx at the point...
find the equation of the tangent line to the curve y=e^-3x • cosx at the point (0,1)
Find the point on the line 3x + y = 5 that is closest to the...
Find the point on the line 3x + y = 5 that is closest to the point (−4, 2). (x, y) =?
Write an equation in slope-intercept form a line that is perpendicular to y = 3x-4 and...
Write an equation in slope-intercept form a line that is perpendicular to y = 3x-4 and that contains (-12, 2). a. y = -1/3 + 2 b. y = -1/3 - 2 c. y = 3x + 26 d. y = 3x + 24
Find the general solution of the given differential equation. (2 + 3x)^2 y'' − 3(2 +...
Find the general solution of the given differential equation. (2 + 3x)^2 y'' − 3(2 + 3x)y' + 9y = 81x   x > − 2/3
Find an equation for the plane containing the line in the xyxy-plane where x=3x=3, and the...
Find an equation for the plane containing the line in the xyxy-plane where x=3x=3, and the line in the yzyz-plane where z=4.5z=4.5.
Find the centroid of the region that is bounded by the line Y = 3X,  the line...
Find the centroid of the region that is bounded by the line Y = 3X,  the line X = 2  and  the X axis.