Given the equation 2x + 8y = 6, answer the following questions:
If x decreases by 2 units, what is the corresponding change in y?
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To find the corresponding change in y when x decreases by 2 units, we need to determine the slope of the equation.
The given equation is in standard form, which is Ax + By = C. We can rewrite the equation in slope-intercept form, y = mx + b, where m represents the slope.
To convert the equation, we isolate y:
2x + 8y = 6
8y = -2x + 6
y = (-2/8)x + 6/8
y = (-1/4)x + 3/4
From the equation, we can see that the slope is -1/4. This means that for every 1 unit change in x, y will change by -1/4 units.
Therefore, if x decreases by 2 units, y will change by (-1/4) * (2) = -1/2 units.
So, the corresponding change in y when x decreases by 2 units is -1/2.
Solve equation for Y
2x + 8y = 6
8y = 6 - 2x
y = 3/4 - x/4
Since this is a straight line, we can pick any value for X. Let's say X=2
Then y(2) = 3/4 - 2/4 = 1/4
Now, decrease x by 2, so x=0
y(0) = 3/4 - 0/4 = 3/4
The difference between Y(0) and Y(2) is
3/4 - 1/4 = 2/4 = 1/2
So the corresponding change in y is +1/2