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

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

Solution

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)