Question Find the value of $y$ when the line $-904-(-38)x=-14y$ has $x=-3$ . (Round answer to two decimal places)

Studdy Solution

STEP 1

Assumptions
1. The equation of the line is $-904-(-38) x=-14 y$ .
2. We are given a specific value for $x$ , which is $x=-3$ .
3. We need to find the corresponding value of $y$ when $x=-3$ .
4. The answer should be rounded to two decimal places.

STEP 2

First, we will simplify the equation of the line by distributing the negative sign inside the parenthesis.
$-904 + 38x = -14y$

STEP 3

Now we will substitute the given value of $x$ into the equation.
$-904 + 38(-3) = -14y$

STEP 4

Multiply $38$ by $-3$ .
$-904 + (-114) = -14y$

STEP 5

Combine the like terms on the left side of the equation.
$-904 - 114 = -14y$

STEP 6

Calculate the sum of $-904$ and $-114$ .
$-1018 = -14y$

STEP 7

Now, we will solve for $y$ by dividing both sides of the equation by $-14$ .
$y = \frac{-1018}{-14}$

STEP 8

Calculate the value of $y$ .
$y = \frac{-1018}{-14} = 72.7142857143$

STEP 9

Round the value of $y$ to two decimal places.
$y \approx 72.71$
The value of $y$ when $x=-3$ is approximately $72.71$ .

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