Question

rewrite the following equations in slope - intercept form to reveal the three letter code. answers must be \all caps\ with no spaces. escape room #2 4. $2y = -x + 8$ 5. $3x = 48 - 8y$ 6. $-5x = -16 - 2y$ g $y=\frac{1}{4}x + 10$ h $y = -\frac{3}{8}x + 6$ i $y=\frac{3}{8}x - 6$ j $y = -\frac{1}{2}x + 4$ k $y = 2x + 4$ l $y=\frac{5}{2}x - 8$ your answer try again!

Explanation:

Step 1: Solve Equation 4 ($2y = -x + 8$)

To convert to slope - intercept form ($y=mx + b$), divide both sides by 2.
$\frac{2y}{2}=\frac{-x + 8}{2}$
$y=-\frac{1}{2}x + 4$
This corresponds to option J.

Step 2: Solve Equation 5 ($3x = 48-8y$)

First, we want to isolate the term with $y$. Add $8y$ to both sides:
$3x+8y=48$
Then subtract $3x$ from both sides:
$8y=-3x + 48$
Divide both sides by 8:
$y=\frac{-3x + 48}{8}=-\frac{3}{8}x+6$
This corresponds to option H.

Step 3: Solve Equation 6 ($-5x=-16 - 2y$)

First, add $2y$ to both sides:
$2y-5x=-16$
Then add $5x$ to both sides:
$2y = 5x-16$
Divide both sides by 2:
$y=\frac{5x-16}{2}=\frac{5}{2}x - 8$
Wait, but let's check the options again. Wait, maybe I made a mistake in equation 6. Let's re - solve equation 6:
Starting with $-5x=-16 - 2y$
Add $2y$ to both sides: $2y-5x=-16$
Add $5x$ to both sides: $2y = 5x-16$
Divide by 2: $y=\frac{5}{2}x-8$, but there is no option with this? Wait, maybe I misread the equation. Wait the equation is $-5x=-16 - 2y$, let's try another way. Let's solve for $y$:
Add $2y$ to both sides: $2y-5x=-16$
Add $5x$: $2y=5x - 16$
$y=\frac{5}{2}x-8$. But the options given: G: $y = \frac{1}{4}x + 10$, H: $y=-\frac{3}{8}x + 6$, I: $y=\frac{3}{8}x-6$, J: $y = -\frac{1}{2}x + 4$, K: $y = 2x+4$, L: $y=\frac{5}{2}x-8$. Oh, option L is $y=\frac{5}{2}x - 8$.

Now, from equation 4 we get J, equation 5 we get H, equation 6 we get L? Wait, no, maybe the three - letter code is from the three equations. Wait the problem says "rewrite the following equations in slope - intercept form to reveal the three - letter code". So equation 4: J, equation 5: H, equation 6: Let's re - check equation 6. Wait the equation is $-5x=-16 - 2y$. Let's move terms:
$2y=5x - 16$
$y=\frac{5}{2}x-8$ which is option L. But the initial equations are 4,5,6. So the three letters from the three equations:

Equation 4: J

Equation 5: H

Equation 6: Wait, maybe I made a mistake in equation 5. Wait equation 5: $3x = 48-8y$

$8y=-3x + 48$

$y=-\frac{3}{8}x + 6$ (option H)

Equation 4: $y = -\frac{1}{2}x+4$ (option J)

Equation 6: Let's solve again: $-5x=-16 - 2y$

Add $2y$ to both sides: $2y-5x=-16$

Add $5x$: $2y=5x - 16$

$y=\frac{5}{2}x-8$ (option L)

But the options for the code: Wait, maybe the three equations are 4,5,6, and their corresponding letters are J, H, L? But let's check the options again. Wait, maybe I misread equation 6. Wait the equation is $-5x=-16 - 2y$, let's try to solve for $y$ by moving $-2y$ to the left and $-5x$ to the right:

$2y=5x - 16$

$y=\frac{5}{2}x-8$ (option L)

Equation 4: J, Equation 5: H, Equation 6: L. But the problem says "three - letter code". Wait, maybe I made a mistake in equation 5. Wait equation 5: $3x = 48-8y$

$8y=48 - 3x$

$y=\frac{48-3x}{8}=6-\frac{3}{8}x=-\frac{3}{8}x + 6$ (option H)

Equation 4: $y=-\frac{1}{2}x + 4$ (option J)

Equation 6: Let's check the equation again. Wait the user's equation for 6 is $-5x=-16 - 2y$. Let's solve for $y$:

$2y=5x - 16$

$y=\frac{5}{2}x-8$ (option L)

So the three - letter code from the three equations (4,5,6) is JHL? Wait, but let's check the options again. Wait, maybe equation 6 is $-5x=-16+2y$? No, the user wrote $-5x=-16 - 2y$.

Wait, maybe I made a mistake in the numbering. Wait the equations are 4,5,6. Let's list the solutions:

Equation 4: $y = -\frac{1}{2}x + 4$ (J)

Equation 5: $y=-\frac{3}{8}x + 6$ (H)

Equation 6: $y=\frac{5}{2}x-8$ (L)

So the three - letter code is JHL? But let's check the options again. Wait, maybe the equation 6 is $-5x=-16 + 2y$? If that's the case, then:

$-5x=-16 + 2y$

$2y=-5x + 16$

$y=-\frac{5}{2}x + 8$, but that's not in the options. So maybe the original equation 6 is $-5x=-16+2y$? No, the user's equation is $-5x=-16 - 2y$.

Wait, maybe I made a mistake in equation 5. Wait equation 5: $3x = 48-8y$

$8y=48 - 3x$

$y = 6-\frac{3}{8}x=-\frac{3}{8}x + 6$ (H)

Equation 4: $y=-\frac{1}{2}x + 4$ (J)

Equation 6: Let's solve $-5x=-16 - 2y$ for $y$:

Add $2y$ to both sides: $2y-5x=-16$

Add $5x$: $2y=5x - 16$

$y=\frac{5}{2}x-8$ (L)

So the three - letter code is JHL? But let's check the options. Wait the options are G, H, I, J, K, L. So J (from 4), H (from 5), L (from 6). So the code is JHL? But let's confirm:

Equation 4: $2y=-x + 8$ → $y = -\frac{1}{2}x + 4$ (J)

Equation 5: $3x=48 - 8y$ → $8y=48 - 3x$ → $y=-\frac{3}{8}x + 6$ (H)

Equation 6: $-5x=-16 - 2y$ → $2y=5x - 16$ → $y=\frac{5}{2}x-8$ (L)

So the three - letter code is JHL. But let's check if we made a mistake in equation 6. Wait, maybe the equation is $-5x=-16 + 2y$? If so:

$-5x=-16 + 2y$ → $2y=-5x + 16$ → $y=-\frac{5}{2}x + 8$, which is not an option. So the correct code from the three equations (4,5,6) is JHL. Wait, but maybe the equations are 4,5, and another? Wait the problem says "the following equations" (4,5,6). So the three - letter code is formed by the letters from each equation's solution. So equation 4: J, equation 5: H, equation 6: L. So the code is JHL.

Wait, but let's re - check equation 6. Let's substitute $x = 0$ into the original equation and the solution. Original equation: $-5(0)=-16-2y$ → $0=-16 - 2y$ → $2y=-16$ → $y=-8$. Our solution: $y=\frac{5}{2}(0)-8=-8$. So the solution is correct. And option L is $y=\frac{5}{2}x - 8$, which matches.

Equation 5: Original equation $3x = 48-8y$. Let's take $x = 0$, then $0=48-8y$ → $8y = 48$ → $y = 6$. Our solution: $y=-\frac{3}{8}(0)+6 = 6$. Correct.

Equation 4: Original equation $2y=-x + 8$. Take $x = 0$, $2y=8$ → $y = 4$. Our solution: $y=-\frac{1}{2}(0)+4 = 4$. Correct.

So the three - letter code is JHL.

Answer:

JHL