Question

In the app you are creating, a duck is going to fly from the coordinates (1, 3) then go 3 units right. And 6 units down. Write a rule to describe the translation. What are the coordinates of the duck's final position?

Answer 1

Answer:

y=-2x+5. (4,-3)

Step-by-step explanation:

1) What's being asked in other words is to write a function. So the initial point is (1,3). In x-axis, a translation movement can only be to the right or to the left. Similarly for y-axis the possible movements are shifting up or down. The question says, 3 units right for x-cordinate and 6 units down for y cordinate. So the final point of this translation would be (1+3,3-6) =(4,-3)

2) To write a linear function we need to find out the slope:

$m=\frac{-3-3}{4-1}=m=\frac{-6}{3} m=-2$

$3=1(-2)+b\\3+2=b\\ b=5\\ \\-3=4(-2)+b\\ b=8-3\\ b=5$

y=-2x+5

Proof:

x=1

y=-2(1)+5

y=3 Then (1,3)

x=4

y=-2(4)+5

y=-8+5

y=-3 Then (4,-3)