Jean wants to translate the line y=4x−5 four units to the left and three units down. How could he correctly perform this transformation?(1 point)
To translate the line y=4x-5 four units to the left and three units down, Jean should subtract 4 from the x-coordinate and subtract 3 from the y-coordinate. Therefore, the translated line would be: y=4(x-4)-5-3.
To correctly perform the given transformation on the line y = 4x - 5, Jean needs to follow these steps:
Step 1: Move four units to the left:
To move the line four units to the left, we need to subtract four from the x-coordinate.
The transformed equation becomes y = 4(x - 4) - 5.
Step 2: Move three units down:
To move the line three units down, we need to subtract three from the y-coordinate.
The transformed equation becomes y - 3 = 4(x - 4) - 5.
Simplifying the equation further, we get:
y - 3 = 4x - 16 - 5
y - 3 = 4x - 21
Therefore, the transformed equation after moving four units to the left and three units down is y - 3 = 4x - 21.
To correctly translate the line y = 4x - 5 four units to the left and three units down, Jean needs to apply the following steps:
1. Translation to the left: To translate four units to the left, you need to subtract 4 from the x-coordinate of each point on the line. This means replacing "x" with "x - 4" in the equation.
Translated equation: y = 4(x - 4) - 5
2. Translation downward: To translate three units down, you need to subtract 3 from the y-coordinate of each point on the line. This simply means subtracting 3 from the y-intercept (-5) in the equation.
Translated equation: y = 4(x - 4) - 5 - 3
3. Simplify: Now, simplify the equation by performing the necessary calculations.
y = 4(x - 4) - 8
Distribute the 4: y = 4x - 16 - 8
Combine like terms: y = 4x - 24
Therefore, the correct translation of the line y = 4x - 5 four units to the left and three units down is y = 4x - 24.