If is a line whose equation is y= 2x - 1, find the equation of the image of under each of the following translations: in book explanation
a. (x, y) S (x, y - 2)
b. (x, y) S (x +3, y)
c. (x, y) S (x - 3, y + 2)
write an equation in slope-intercept form for the line that satisfies the following condition. Pass through (11, -15) & (16, 5)
521
To find the equation of the image of a line under each of the given translations, we need to transform the given line according to the translation rules. Let's go through each translation step by step:
a. (x, y) S (x, y - 2):
In this translation, the y-coordinate of every point is shifted downward by 2 units. To obtain the equation of the image, we need to modify the equation of the original line accordingly by subtracting 2 from the y-coordinate.
The original equation of the line is y = 2x - 1. By substituting y - 2 for y in the equation, we get:
y - 2 = 2x - 1
Simplifying the equation, we have:
y = 2x + 1
Therefore, the equation of the image of the line under this translation is y = 2x + 1.
b. (x, y) S (x + 3, y):
In this translation, the x-coordinate of every point is shifted to the right by 3 units. To obtain the equation of the image, we need to modify the equation of the original line accordingly by replacing x with (x + 3).
The original equation of the line is y = 2x - 1. By substituting (x + 3) for x in the equation, we get:
y = 2(x + 3) - 1
Expanding and simplifying the equation, we have:
y = 2x + 6 - 1
y = 2x + 5
Therefore, the equation of the image of the line under this translation is y = 2x + 5.
c. (x, y) S (x - 3, y + 2):
In this translation, the x-coordinate of every point is shifted to the left by 3 units, and the y-coordinate is shifted upward by 2 units. To obtain the equation of the image, we need to modify the equation of the original line accordingly by replacing x with (x - 3) and y with (y + 2).
The original equation of the line is y = 2x - 1. By substituting (x - 3) for x and (y + 2) for y in the equation, we get:
(y + 2) = 2(x - 3) - 1
Expanding and simplifying the equation, we have:
y + 2 = 2x - 6 - 1
y + 2 = 2x - 7
y = 2x - 7 - 2
y = 2x - 9
Therefore, the equation of the image of the line under this translation is y = 2x - 9.
That's how you can find the equation of the image of a line under different translations.