Given the equation 2x + 10y = 10, answer the following questions:
If x decreases by 2 units, what is the corresponding change in y?
? units
2x + 10y = 10.
When x = 0, Y = 1.
When x = 0-2 = -2, Y = 1.4.
Change in y = 1.4-1 = 0.4 Units.
To find the corresponding change in y when x decreases by 2 units in the equation 2x + 10y = 10, we can solve for y in terms of x.
First, let's rearrange the equation:
2x + 10y = 10
Subtract 2x from both sides:
10y = 10 - 2x
Divide both sides by 10:
y = (10 - 2x) / 10
Now we can substitute x - 2 into the equation for x and solve for y:
y = (10 - 2(x - 2)) / 10
Simplifying this equation, we get:
y = (10 - 2x + 4) / 10
y = (14 - 2x) / 10
y = 7/5 - (1/5) * x
Now we can see that when x decreases by 2 units, the corresponding change in y is given by:
Change in y = (1/5) * (change in x)
Since x decreases by 2 units, the change in x is -2. Therefore,
Change in y = (1/5) * (-2)
Change in y = -2/5
So, the corresponding change in y when x decreases by 2 units is -2/5 units.