SOLUTION: Find the equation of the line 𝑦=(3/2)x+1 translated through a vector (-2, -2). Also sketch it.

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Question 1157499: Find the equation of the line 𝑦=(3/2)x+1 translated through a vector (-2, -2). Also sketch it.
Found 2 solutions by KMST, greenestamps:
Answer by KMST(5420) About Me  (Show Source):
You can put this solution on YOUR website!
Translating the line y=%283%2F2%29x%2B1 will not change the slope=3%2F2 .
every point in the line will be translates 2 units down and 2 units to the left.
It will translate the point P%280%2C1%29 to Q , with coordinates
x%5BQ%5D=0-2=-2 and y%5BQ%5D=1-2=-1
The equation for the new line will be
y-%28-1%29=%283%2F2%29%28x-%28-2%29%29 ---> y%2B1=%283%2F2%29x%2B2%29 --> y=%283%2F2%29x%2B2%283%2F2%29-1 --> y=%283%2F2%29x%2B3-1 --> highlight%28y=%283%2F2%29x%2B2%29

Answer by greenestamps(13374) About Me  (Show Source):
You can put this solution on YOUR website!


Less formally than in the solution by tutor KMST....

The given line has the equation y=%283%2F2%29x%2B1.

Translating the line through the vector (-2,-2) does not change the slope; it will (probably, at least) change the y-intercept.

The translation moves each point on the line left 2 and down 2. To find the y-intercept of the translated line, find the point on the given line with x=2 and translate that point left 2 and down 2.

y=%283%2F2%29%282%29%2B1=3%2B1=4

The point on the given line with x=2 is (2,4).

Translate that point left 2 and down 2 to find the y-intercept of the translated line: (2-2,4-2) = (0,2).

The translated line has slope (3/2) and y-intercept (0,2).

The equation of the translated line is

ANSWER: y=%283%2F2%29x%2B2