The equation of this graph is y= 2/3-4 what transformation would need to happen for the equation of the line to be y=2/3x
To transform the equation y = 2/3 - 4 into y = 2/3x, you need to perform the following steps:
1) Move the constant term to the other side of the equation:
y + 4 = 2/3
2) To simplify the equation, multiply both sides by 3 to get rid of the fraction:
3(y + 4) = 2
3) Distribute 3 to both terms within the parentheses:
3y + 12 = 2
4) Move the constant term to the other side of the equation:
3y = 2 - 12
3y = -10
5) Divide both sides by 3 to solve for y:
y = -10/3
Thus, the transformation required is y = 2/3 - 4 becomes y = -10/3.
To transform the equation y = 2/3 - 4 into y = (2/3)x, we need to perform the following steps:
Step 1: Remove the constant term from the original equation.
- Subtracting 4 from both sides yields: y + 4 = 2/3
Step 2: Isolate the variable 'y.'
- Subtract 4 from both sides again to remove the constant: y = 2/3 - 4
or y = (2/3)x
Therefore, to transform the equation y = 2/3 - 4 into y = (2/3)x, we need to subtract 4 from both sides.
To transform the equation y = (2/3) - 4 to y = (2/3)x, we need to understand the differences between the two equations and identify the required transformations.
Starting with the given equation y = (2/3) - 4, let's break it down:
1. The constant term: The given equation has a constant term of -4, which means that the graph is shifted downward by 4 units compared to the equation y = (2/3)x. To move the graph up by 4 units, we need to add 4 to the equation.
2. The slope: In the given equation, the slope is 0 since (2/3) - 4 is a constant. However, in the desired equation y = (2/3)x, the slope is (2/3), which means the graph is steeper. To achieve this, we need to multiply the equation by (2/3).
Applying these transformations to the given equation, we can rewrite it as follows:
y = (2/3) - 4
Adding 4 to both sides:
y + 4 = (2/3) - 4 + 4
y + 4 = (2/3)
Subtracting 4 from both sides:
y + 4 - 4 = (2/3) - 4
y = (2/3) - 4
Finally, the transformation required to make the equation y = (2/3) - 4 into y = (2/3)x involves shifting the graph up by 4 units and multiplying the equation by (2/3).