Given the equation 2x + 7y = 4, if x decreases by 4 units, what is the corresponding change in y?

Question

Quizplus · Accepted Answer

To solve this problem using the given equation, we need to find the relationship between x and y.

First, isolate y:

2x + 7y = 4

7y = -2x + 4

y = (-2/7)x + 4/7

This tells us that the relationship between x and y is that y decreases as x increases (since the coefficient of x is negative).

So if x decreases by 4 units, we would expect y to increase by some amount.

To find out how much y increases, substitute x-4 into the equation for x:

y = (-2/7)(x-4) + 4/7

This simplifies to:

y = (-2/7)x + (8/7) + 4/7

y = (-2/7)x + 12/7

Now we can see that for every one unit decrease in x, y increases by 2/7.

So if x decreases by 4 units, y will increase by:

(2/7) x 4 = 8/7

Therefore, the corresponding change in y is 8/7 or approximately 1.14.

The closest answer choice is B, which is 11eb12b0_aa75_733f_b394_4d5173297b76_TB7866_11.

Given the Equation 2x + 7y = 4, If X