In y=4x, what happen to y when x is doubled? increased by 2? decreased by 3? halved?
In y=4x, what happen to y when x is doubled? increases by 2? decreased by 3? halved?
In y=4x, double x, one has to double y.
Try it x=1, then x=2, then x=4 See if y doubles each time.
To answer the first question, we need to understand the relationship between x and y in the equation y = 4x. The equation tells us that y is equal to four times x.
When x is doubled, we can simply multiply the original value of y by 2 because y is directly proportional to x. So, if we start with x = 1, then double it to x = 2, we can find y by multiplying the original y value by 2. In this case, for x = 1, y = 4(1) = 4, and for x = 2, y = 4(2) = 8. As we can see, y doubles when x is doubled.
To answer the second question, we need to apply the same principles. If we increase x by 2, y will also increase by 2 times the coefficient (4). For example, if we start with x = 1, then increase it by 2 to x = (1 + 2) = 3, we can find y by multiplying the original y value by 3. In this case, for x = 1, y = 4(1) = 4, and for x = 3, y = 4(3) = 12. As we can see, y increases by 2 times the increment in x.
For the third question, if we decrease x by 3, y will also decrease by 3 times the coefficient (4). For example, if we start with x = 1, then decrease it by 3 to x = (1 - 3) = -2, we can find y by multiplying the original y value by -2. In this case, for x = 1, y = 4(1) = 4, and for x = -2, y = 4(-2) = -8. As we can see, y decreases by 3 times the decrement in x.
Lastly, if we halve x, y will also halve because y is directly proportional to x. For example, if we start with x = 2, then halve it to x = (2/2) = 1, we can find y by halving the original y value. In this case, for x = 2, y = 4(2) = 8, and for x = 1, y = (8/2) = 4. As we can see, y is halved when x is halved.
In summary:
- When x is doubled, y doubles.
- When x is increased by 2, y increases by 2 times the coefficient.
- When x is decreased by 3, y decreases by 3 times the coefficient.
- When x is halved, y is halved.